Matej Brešar
Oddelek za matematiko/Department of Mathematics
Fakulteta za matematiko in fiziko/Faculty of Mathematics and Physics
Univerza v Ljubljani/University of Ljubljana
matej.bresar@fmf.uni-lj.si
in/and
Oddelek za matematiko in računalništvo/Department of Mathematics and Computer Science
Fakulteta za naravoslovje in matematiko/Faculty of Natural Sciences and Mathematics
Univerza v Mariboru/University of Maribor
matej.bresar@um.si
Knjige/Books
Poljudni članek
Besedilo nastopnega predavanja na Slovenski akademiji znanosti in umetnosti (11. april 2017)
(pdf)
Uredniški odbori/Editorial Boards
Članki/Papers
- Functional identities and their applications, Bull. Math. Sci. 2330002, 73pp.
(pdf)
- Derivations and homomorphisms in commutator-simple algebras, Proc. Amer. Math. Soc. 151 (2023), 4721-4733 (with J. Alaminos, J. Extremera, M. L. C. Godoy and A. R. Villena)
(pdf)
- The Waring problem for matrix algebras, II, Bull. London Math. Soc. 55 (2023), 1880-1889 (with P. Šemrl)
(pdf)
- The Waring problem for matrix algebras, Israel J. Math. 253 (2023), 381-405 (with P. Šemrl)
(pdf)
- Functional identities and maps preserving two-sided zero products, in Algebraic, Number Theoretic, and Toplogical Aspects of Ring Theory, 113-133, Springer, 2023.
- Weighted Jordan homomorphisms, Linear Multilinear Algebra 8 (2023), 1265–1279 (with M. L. C. Godoy)
(pdf)
- Automorphisms and derivations of finite-dimensional algebras, J. Algebra 599 (2022), 104–121.
(pdf)
- Maps preserving two-sided zero products on Banach algebras, J. Math. Anal. Appl. 515 (2022), 126372, 16 pp. (with M. L. C. Godoy and A. R. Villena)
(pdf)
- Two-sided zero product determined algebras, Linear Algebra Appl. 643 (2022), 125-136 (with Ž. Bajuk)
(pdf)
- On, around, and beyond Frobenius' theorem on division algebras, Linear Multilinear Algebra 7 (2022), 1369-1381 (with V. Shulman)
(pdf)
- Jordan maps and zero Lie product determined algebras, Turkish J. Math. 46 (2022), 1691–1698.
(pdf)
- Zero Jordan product determined Banach algebras, J. Austral. Math. Soc. 111 (2021), 145-158
(with J. Alaminos, J. Extremera, and A. R. Villena) (pdf)
- Commutators and images of noncommutative polynomials, Adv. Math. 374 (2020), 107346, 21pp.
(pdf)
- Functional identities and zero Lie product determined Banach algebras, Quart. J. Math. 71 (2020), 649-665
(pdf)
- Zero product determined maps on matrix rings over division rings, Contemporary Math. 750 (2020), 195-213
(with P. Šemrl) (pdf)
- Centrally stable algebras, J. Algebra 537 (2019), 79–97 (with I. Gogić) (pdf)
- Zero Lie product determined Banach algebras, II, J. Math. Anal. Appl. 474 (2019), 1498-1511
(with J. Alaminos, J. Extremera, and A. R. Villena) (pdf)
- Zero product determined Lie algebras, European J. Math. 5 (2019), 424-453
(with X. Guo, G. Liu, R. Lü, and K. Zhao)
(pdf)
- Continuous commuting functions on matrix algebras, Linear Algebra Appl. 568 (2019), 29-38 (with P. Šemrl)
(pdf)
- Biderivations and commuting linear maps on Lie algebras, J. Lie Theory 28 (2018), 885-900 (with K. Zhao)
(pdf)
- Skolem-Noether algebras, J. Algebra 498 (2018), 294-314 (with C. Hanselka, I. Klep, and J. Volčič)
(pdf)
- Zero Lie product determined Banach algebras, Studia Math. 239 (2017), 189-199 (with J. Alaminos, J. Extremera, and A. R. Villena)
(pdf)
- Derivations of tensor products of nonassociative algebras, Linear Algebra Appl. 530 (2017), 244-252
(pdf)
- Functional identities and rings of quotients, Algebras Represent. Theory 19 (2016), 1437-1450 (pdf)
- Jordan {g, h}-derivations on tensor products of algebras, Linear Multilinear Algebra 64 (2016), 2199-2207
(pdf)
- Orthogonally additive polynomials and orthosymmetric maps in Banach algebras with properties A and B, Proc. Edinb. Math. Soc. 59 (2016), 559-568
(with J. Alaminos, Š. Špenko, and A. R. Villena) (pdf)
- Commutators and square-zero elements in Banach algebras, Quart. J. Math. 67 (2016),
1-13 (with J. Alaminos, J. Extremera, Š. Špenko, and A. R. Villena)
(pdf)
- Functional identities on tensor products of algebras, J. Algebra 455 (2016), 108-136
(pdf)
- Finite dimensional zero product determined algebras are generated by idempotents, Expo. Math. 34 (2016), 130-143
(pdf)
- Quasi-identities on matrices and the Cayley-Hamilton polynomial, Adv. Math. 280 (2015), 439-471 (with C. Procesi and Š. Špenko)
(pdf)
- Functional Identities on matrix algebras, Algebr. Represent. Theory 18 (2015), 1337-1356 (with Š. Špenko)
(pdf)
- Algebras in which non-scalar elements have small centralizers, Linear Multilinear Algebra 63 (2015), 1864-1871
(pdf)
- Derivations preserving quasinilpotent elements, Bull. London Math. Soc. 46 (2014), 379-384
(with J. Alaminos, J. Extremera, Š. Špenko, and A. R. Villena)
(pdf)
- Functional identities in one variable, J. Algebra 401 (2014), 234-244 (with Š. Špenko) (pdf)
- A local-global principle for linear dependence of noncommutative polynomials, Israel J. Math. 193 (2013), 71-82 (with I. Klep)
(pdf)
- Central polynomials for matrices over finite fields, Linear and Multilinear Algebra 61 (2013), 939-944 (with V. Drensky)
(pdf)
- Determining elements in C*-algebras through spectral properties, J. Math. Anal. Appl. 405 (2013), 214-219
(with J. Alaminos, J. Extremera, Š. Špenko, and A. R. Villena) (pdf)
- A unified approach to the structure theory of PI-rings and GPI-rings, Serdica Math. J. 38 (2012), 199-210
(pdf)
- On maps determined by zero products, Comm. Algebra 40 (2012), 2081-2090 (with H. Bierwirth and M. Grašič)
(pdf)
- Group gradings on finitary simple Lie algebras, International Journal of Algebra and Computation 22 (2012), 1250046 (with Y. Bahturin and
M. Kochetov) (pdf)
- Identifying derivations through the spectra of their values, Integr. Eq. Oper. Th. 73 (2012), 395-411 (with B. Magajna and Š. Špenko)
(pdf)
- Multiplication algebra and maps determined by zero products, Linear Multilinear Algebra 60 (2012), 763-768
(pdf)
- Lie superautomorphisms on associative algebras, II, Algebras Repr. Th. 15 (2012), 507-525 (with Y. Bahturin and Š. Špenko)
(pdf)
- Determining elements in Banach algebras through spectral properties, J. Math. Anal. Appl. 393 (2012), 144-150 (with Š. Špenko)
(pdf)
- On Lie and associative algebras containing inner derivations, Linear Algebra Appl. 437 (2012), 648-658 (with Š. Špenko)
(pdf)
- Maps preserving zeros of a polynomial, Linear Algebra Appl. 436 (2012), 2504-2512 (with J. Alaminos, Š. Špenko, and A. R. Villena)
(pdf)
- A note on spectrum-preserving maps, J. Math. Anal. Appl. 387 (2012), 595-603 (with J. Alaminos, P. Šemrl, and A. R. Villena)
(pdf)
- Tracial Nullstellensatze, in Notions of Positivity and the Geometry of Polynomials, Trends in Mathematics (2011), 79-101 (with I. Klep)
(pdf)
- An alternative approach to the structure theory of PI-rings, Expo. Math. 29 (2011), 159-164
(pdf)
- Jordan gradings on associative algebras, Algebras Repr. Th. 14 (2011),113-129 (with Y. Bahturin and I. Shestakov)
(pdf)
- On locally complex algebras and low-dimensional Cayley-Dickson algebras, J. Algebra 327 (2011), 107-125 (with P. Šemrl and Š. Špenko)
(pdf)
- On a class of finitary Lie algebras characterized through derivations, Proc. Amer. Math. Soc. 138 (2010), 4161-4166
(with A. Fernandez Lopez) (pdf)
- Characterizing Jordan maps on C*-algebras through zero products, Proc. Edinb. Math. Soc. 53 (2010), 543-555
(with J. Alaminos, J. Extremera, and A. R. Villena) (pdf)
- On bilinear maps determined by rank one idempotents, Linear Algebra Appl. 432 (2010), 738-743 (with J. Alaminos,
J. Extremera, and A. R. Villena)(pdf)
- Lie superautomorphisms on associative algebras, Proc. Amer. Math. Soc. 138 (2010), 417-425 (with Y. Bahturin)
(pdf)
- On tractability and ideal problem in non-associative operator algebras, Integr. Eq. Oper. Th. 67 (2010), 279-300
(with. V. Shulman and Y. Turovskii) (pdf)
- A note on values of noncommutative polynomials, Proc. Amer. Math. Soc. 138 (2010), 2375-2379 (with I. Klep)
(pdf)
- An elementary approach to Wedderburn's structure theory, Expo. Math. 28 (2010), 79-83
(pdf)
- Values of noncommutative polynomials, Lie skew-ideals and tracial Nullstellensatze, Math. Res. Letters 16 (2009), 605-626 (with I. Klep)
(pdf)
- Computing the maximal algebra of quotients of a Lie algebra, Forum Math. 21 (2009), 601-620 (with F. Perera, J. Sanchez, and M. Siles)
(pdf)
- Maps preserving zero products, Studia Math. 193 (2009), 131-159 (with J. Alaminos, J. Extremera, and A. R. Villena)
(pdf)
- Lie gradings on associative algebras, J. Algebra 321 (2009), 264-283 (with Y. Bahturin)
(pdf)
- Polynomially compact derivations on Banach algebras, Stud. Math. 190 (2009), 185-191 (with Y. Turovskii)
(pdf)
- Zero product determined matrix algebras, Linear Algebra Appl. 430 (2009), 1486-1498 (with M. Grašič and J. Sanchez)
(pdf)
- Range-inclusive maps in rings with idempotents, Comm. Algebra 37 (2009), 154-163.
- When Jordan submodules are bimodules, Quart. J. Math. 59 (2008), 409-440 (with E. Kissin and V. Shulman)
(pdf)
- Near-derivations in Lie algebras, J. Algebra 320 (2008), 3765-3772
(pdf)
- Lie ideals: from pure algebra to C*-algebras, J. Reine Angew. Math. 623 (2008), 73-121 (with E. Kissin and V. Shulman)
(pdf)
- Zero product preserving maps on C^1[0,1], J. Math. Anal. Appl. 347 (2008), 472-481 (with J. Alaminos, M. Černe, J. Extremera,
and A. R. Villena) (pdf)
- Jordan homomorphisms revisited, Math. Proc. Camb. Phil. Soc. 144 (2008), 317-328
(pdf)
- An extension of the Gleason-Kahane-Zelazko theorem: a possible approach to Kaplansky's problem, Expo. Math. 26 (2008), 269-277 (with P. Šemrl).
- On Jordan ideals and submodules: algebraic and analytical aspects, Funct. Anal. Appl. 42 (2008), 220-223 (with E. Kissin and V. Shulman).
- Commutativity preserving maps revisited, Israel J. Math. 162 (2007), 317-334.
- Compactness conditions for elementary operators, Stud. Math. 178 (2007), 1-18 (with Y. Turovskii)
(pdf)
- Characterizing homomorphisms, derivations and multipliers in rings with idempotents, Proc. Royal Soc. Edinb. Sect. A 137 (2007), 9-21
(pdf)
- Characterizing homomorphisms and derivations on C*-algebras, Proc. Royal Soc. Edinb. Sect. A 137 (2007), 1-7 (with J. Alaminos, J. Extremera, and A. R. Villena).
- On bilinear maps on matrices with applications to commutativity preservers, J. Algebra 301 (2006), 803-837 (with P. Šemrl).
- On the multiplication ring of a prime ring, Comm. Algebra 34 (2006), 2195-2203 (with W. S. Martindale).
- Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan-Banach algebras, Studia Math. 169 (2005), 207-228 (with M. Cabrera, M. Fošner and A. R. Villena).
- Jordan derivations revisited, Math. Proc. Camb. Phil. Soc. 139 (2005), 411-425
(pdf)
- The range and kernel inclusion of algebraic derivations and commuting maps, Quart. J. Math. 56 (2005), 31-41.
- Jordan ideals revisited, Monatsh. Math. 145 (2005), 1-10 (with A. Fošner and M. Fošner).
- Commutativity preserving linear maps on central simple algebras, J. Algebra 284 (2005), 102-110 (with P. Šemrl).
- Elementary operators as Lie homomorphisms or commutativity preservers, Proc. Edinb. Math. Soc. 48 (2005), 37-49 (with P. Šemrl).
- Commuting maps: A survey, Taiwan. J. Math. 8 (2004), 361-397.
- The strong degree of von Neumann algebras and the structure of Lie and Jordan derivations, Math. Proc. Camb. Phil. Soc. 137 (2004), 441-463 (with J. Alaminos and A.R. Villena).
- On commutators and derivations in rings, J. Algebra 278 (2004), 704-724 (with D. Eremita and T.-L. Wong).
- Polynomial preserving maps on certain Jordan algebras, Israel J. Math. 141 (2004), 285-313 (with K.I. Beidar, M. A. Chebotar, and W. S. Martindale).
- Commuting traces of biadditive maps revisited, Comm. Algebra 31 (2003), 381-388 (with P. Šemrl).
- A note on invertibility preservers on Banach algebras, Proc. Amer. Math. Soc. 131 (2003), 3833-3837 (with A. Fošner and P. Šemrl).
- Functional identities in Jordan algebras: Associating traces and Lie triple isomorphisms, Comm. Algebra 31 (2003), 1207-1234 (with D. Eremita and A. R. Villena).
- The lower socle and finite rank elementary operators, Comm. Algebra 31 (2003), 1485-1497 (with D. Eremita).
- On d-free rings, Comm. Algebra 31 (2003), 2287-2309.
- Jordan superhomomorphisms, Comm. Algebra 31 (2003), 633-644 (with K. I. Beidar and M. A. Chebotar)
(pdf)
- The noncommutative Singer-Wermer conjecture and phi-derivations, J. London Math. Soc. 66 (2002), 710-720 (with A. R. Villena).
- On a certain functional identity in prime rings, II, Beitr. Alg. Geom. 43 (2002), 333-338 (with M. A. Chebotar).
- Functional identities in Jordan algebras: Associating maps, Comm. Algebra 30 (2002), 5241-5252 (with M. Cabrera and A. R. Villena).
- On automorphisms of Banach algebras, Arch. Math. 78 (2002), 297-302.
- Applying functional identities to some linear preserver problems, Pacific J. Math. 204 (2002), 257-271 (with K. I. Beidar, M. A. Chebotar, and Y. Fong).
- Functional identities with r-independent coefficients, Comm. Algebra 30 (2002), 5725-5755 (with K. I. Beidar and M. A. Chebotar).
- Functional identities revised: the fractional and the strong degree, Comm. Algebra 30 (2002), 935-969 (with K.I. Beidar and M. A. Chebotar).
- On Herstein's Lie map conjectures, III, J. Algebra 249 (2002), 59-94 (with K.I. Beidar, M. A. Chebotar, and W. S. Martindale).
- On Herstein's Lie map conjectures, II, J. Algebra 238 (2001), 239-264 (with K.I. Beidar, M. A. Chebotar, and W. S. Martindale).
- Extended Jacobson density theorem for Lie ideals of rings with automorphisms, Publ. Math. Debrecen 58 (2001), 325-335 (with K.I. Beidar and Y. Fong).
- A Kleinecke-Shirokov type condition with Jordan automorphisms, Studia Math. 147 (2001), 237-242 (with A. Fošner and M. Fošner).
- The range of a derivation on a Jordan-Banach algebra, Studia Math. 146 (2001), 177-200 (with A. R. Villena).
- On Herstein's Lie map conjectures, I, Trans. Amer. Math. Soc. 353 (2001), 4235-4260 (with K.I. Beidar, M. A. Chebotar, and W. S. Martindale).
- Extended Jacobson density theoremfor rings with derivations and automorphisms, Israel J. Math. 122 (2001), 317-346 (with K.I. Beidar).
- Functional identities: A survey, Contemporary Math. 259 (2000), 93-109
(pdf)
- Functional identities on upper triangular matrix algebras, J. Math. Sci. 102 (2000), 4557-4565 (with K.I. Beidar and M. A. Chebotar).
- Elementary operators, II, Acta Sci. Math. 66 (2000), 769-791 (with L. Molnar and P. Šemrl).
- On functional identities in prime rings with involution II, Comm. Algebra 28 (2000), 3169-3183 (with K.I. Beidar, M.A. Chebotar, and W.S. Martindale).
- Applying the density theorem for derivations to range inclusion problems, Studia Math. 138 (2000), 93-100 (with K. I. Beidar).
- On rings with involution equipped with some new product, Publ. Math. Debrecen 57 (2000), 121-134 (with M. Fošner).
- Jordan isomorphisms of triangular matrix algebras over a connected commutative ring, Linear Algebra Appl. 312 (2000), 197-201 (with K.I. Beidar and M.A. Chebotar).
- On derivations of prime rings, Comm. Algebra 27 (1999), 3129-3135 (with M.A. Chebotar and P. Šemrl).
- Generalized functional identities with (anti)automorphisms and derivations on prime rings, J. Algebra 215 (1999), 644-665 (with K.I. Beidar and M.A. Chebotar).
- On locally linearly dependent operators and derivations, Trans. Amer. Math. Soc. 351 (1999), 1257-1275 (with P. Šemrl).
- Elementary operators, Proc. Royal Soc. Edinburgh Sect. A 129 (1999), 1115-1135 (with P. Šemrl).
- Spectral characterization of idempotents and invertibility preserving linear maps, Expo. Math. 17 (1999), 185-192 (with P. Šemrl).
- On additive maps of prime rings, II, Publ. Math. Debrecen 54 (1999), 39-54 (with B. Hvala).
- On a certain functional identity in prime rings, Comm. Algebra 26 (1998), 3765-3781 (with M. A. Chebotar).
- Invertibility preserving maps preserve idempotents, Michigan J. Math. 45 (1998), 483-488 (with P. Šemrl).
- Dependent automorphisms in prime rings, Canad. Math. Bull. 41 (1998), 452-462 (with W. S. Martindale and C. R. Miers).
- Maps preserving nth powers, Comm. Algebra 26 (1998), 117-138 462 (with W. S. Martindale and C. R. Miers).
- Finite rank elements in semisimple Banach algebras, Studia Math. 128 (1998), 287-298 (with P. Šemrl).
- On certain pairs of automorphisms of rings, II, J. Austral. Math. Soc. 64 (1998), 162-168.
- Derivations mapping into the socle, II, Proc. Amer. Math. Soc. 126 (1998), 181-187.
- Linear preservers on B(X), Banach Center Publ. 38 (1997), 49-58 (with P. Šemrl).
- On a certain identity satisfied by a derivation and an arbitrary additive mapping II, Aequationes Math. 51 (1996), 83-85.
- Derivations mapping into the socle, Math. Proc. Camb. Phil. Soc. 120 (1996), 339-346 (with P. Šemrl).
- Spectral characterizations of central elements in Banach algebras, Studia Math. 120 (1996), 47-52 (with P. Šemrl).
- On local automorphisms and mappings that preserve idempotents, Studia Math. 113 (1995), 101-108 (with P. Šemrl).
- Linear maps preserving the spectral radius, J. Funct. Anal. 142 (1996), 360-368 (with P. Šemrl).
- Commuting maps on Lie ideals, Comm. Algebra 23 (1995), 5539-5553 (with C. R. Miers).
- Derivations mapping into the radical, III, J. Funct. Anal. 133 (1995), 21-29 (with M. Mathieu).
- On additive maps of prime rings, Bull. Austral. Math. Soc. 51 (1995), 377-381 (with B. Hvala).
- Applying the theorem on functional identities, Nova J. Math. Game Th. Alg. 4 (1995), 43-54.
- On generalized biderivations and related maps, J. Algebra 172 (1995), 764-786.
- Functional identities of degree two, J. Algebra 172 (1995), 690-720.
- Strong commutativity preserving maps of semiprime rings, Canad. Math. Bull. 37 (1994), 457-460 (with C. R. Miers).
- Derivations of noncommutative Banach algebras II, Arch. Math. 63 (1994), 56-59.
- One-sided ideals and derivations of prime rings, Proc. Amer. Math. Soc. 122 (1994), 979-983.
- Normal-preserving linear mappings, Canad. Math. Bull. 37 (1994), 306-309 (with P. Šemrl).
- On certain pairs of functions of semiprime rings, Proc. Amer. Math. Soc. 120 (1994), 709-713.
- On a certain identity satisfied by a derivation and an arbitrary additive mapping, Aequationes Math. 45 (1993), 219-231 (with J. Škarabot and J. Vukman}.
- On certain subrings of prime rings with derivations, J. Austral. Math. Soc. 54 (1993), 133-141 (with J. Vukman).
- Linear transformations preserving potent matrices, Proc. Amer. Math. Soc. 119 (1993), 81-86 (with P. Šemrl).
- Mappings which preserve idempotents, local automorphisms, and local derivations, Canad. J. Math. 45 (1993), 483-496 (with P. Šemrl).
- On some identities in prime rings with involution, Comm. Algebra 21 (1993), 4679-4697 (with W. S. Martindale and C. R. Miers).
- Commutativity preserving mappings of von Neumann algebras, Canad. J. Math. 45 (1993), 695-708 (with C. R. Miers).
- Centralizing maps in prime rings with involution, J. Algebra 161 (1993), 342-357 (with W. S. Martindale and C. R. Miers).
- Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings,Trans. Amer. Math. Soc. 335 (1993), 525-546.
- Derivations decreasing the spectral radius, Arch. Math. 61 (1993), 160-162.
- On skew-commuting mappings of rings, Bull. Austral. Math. Soc. 47 (1993), 291-296.
- Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), 385-394.
- On certain pairs of automorphisms of rings, J. Austral. Math. Soc. 54 (1993), 29-38.
- On the structure of Jordan *-derivations, Colloq. Math. 63 (1992), 163-171 (with B. Zalar).
- Derivations of noncommutative Banach algebras, Arch. Math. 59 (1992), 363-370 (with J. Vukman).
- On the compositions of (alpha,beta)-derivations of rings, and applications to von Neumann algebras, Acta. Sci. Math. 56 (1992), 369-375.
- Characterizations of derivations on some normed algebras with involution, J. Algebra 152 (1992), 454-462.
- On a generalization of the notion of centralizing mappings, Proc. Amer. Math. Soc. 114 (1992), 641-649.
- Jordan (theta, phi)-derivations, Glasnik Mat. 26 (1991), 13-17 (with J. Vukman).
- Jordan mappings of semiprime rings II, Bull. Austral. Math. Soc. 44 (1991), 233-238.
- Centralizing mappings on von Neumann algebras, Proc. Amer. Math. Soc. 111 (1991), 501-510.
- On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89-93.
- A note on derivations, Math. J. Okayama Univ. 32 (1990), 83-88.
- On left derivations and related mappings, Proc. Amer. Math. Soc. 110 (1990), 7-16 (with J. Vukman).
- Semiderivations of prime rings, Proc. Amer. Math. Soc. 108 (1990), 859-860.
- On some additive mappings in rings with involution, Aequationes Math. 38 (1989), 178-185 (with J. Vukman).
- Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228.
- Orthogonal derivations and an extension of a theorem of Posner, Rad. Mat. 5 (1989), 237-246 (with J. Vukman).
- Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006.
- Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-322 (with J. Vukman).