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)

Članki/Papers

  1. 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)
  2. Zero product determined Lie algebras, European J. Math. 5 (2019), 424-453 (with X. Guo, G. Liu, R. Lü, and K. Zhao) (pdf)
  3. Continuous commuting functions on matrix algebras, Linear Algebra Appl. 568 (2019), 29-38 (with P. Šemrl) (pdf)
  4. Biderivations and commuting linear maps on Lie algebras, J. Lie Theory 28 (2018), 885-900 (with K. Zhao) (pdf)
  5. Skolem-Noether algebras, J. Algebra 498 (2018), 294-314 (with C. Hanselka, I. Klep, and J. Volčič) (pdf)
  6. Zero Lie product determined Banach algebras, Studia Math. 239 (2017), 189-199 (with J. Alaminos, J. Extremera, and A. R. Villena) (pdf)
  7. Derivations of tensor products of nonassociative algebras, Linear Algebra Appl. 530 (2017), 244-252 (pdf)
  8. Functional identities and rings of quotients, Algebras Represent. Theory 19 (2016), 1437-1450 (pdf)
  9. Jordan {g, h}-derivations on tensor products of algebras, Linear Multilinear Algebra 64 (2016), 2199-2207 (pdf)
  10. 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)
  11. 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)
  12. Functional identities on tensor products of algebras, J. Algebra 455 (2016), 108-136 (pdf)
  13. Finite dimensional zero product determined algebras are generated by idempotents, Expo. Math. 34 (2016), 130-143 (pdf)
  14. Quasi-identities on matrices and the Cayley-Hamilton polynomial, Adv. Math. 280 (2015), 439-471 (with C. Procesi and Š. Špenko) (pdf)
  15. Functional Identities on matrix algebras, Algebr. Represent. Theory 18 (2015), 1337-1356 (with Š. Špenko) (pdf)
  16. Algebras in which non-scalar elements have small centralizers, Linear Multilinear Algebra 63 (2015), 1864-1871 (pdf)
  17. Derivations preserving quasinilpotent elements, Bull. London Math. Soc. 46 (2014), 379-384 (with J. Alaminos, J. Extremera, Š. Špenko, and A. R. Villena) (pdf)
  18. Functional identities in one variable, J. Algebra 401 (2014), 234-244 (with Š. Špenko) (pdf)
  19. A local-global principle for linear dependence of noncommutative polynomials, Israel J. Math. 193 (2013), 71-82 (with I. Klep) (pdf)
  20. Central polynomials for matrices over finite fields, Linear and Multilinear Algebra 61 (2013), 939-944 (with V. Drensky) (pdf)
  21. 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)
  22. A unified approach to the structure theory of PI-rings and GPI-rings, Serdica Math. J. 38 (2012), 199-210 (pdf)
  23. On maps determined by zero products, Comm. Algebra 40 (2012), 2081-2090 (with H. Bierwirth and M. Grašič) (pdf)
  24. Group gradings on finitary simple Lie algebras, International Journal of Algebra and Computation 22 (2012), 1250046 (with Y. Bahturin and M. Kochetov) (pdf)
  25. Identifying derivations through the spectra of their values, Integr. Eq. Oper. Th. 73 (2012), 395-411 (with B. Magajna and Š. Špenko) (pdf)
  26. Multiplication algebra and maps determined by zero products, Linear Multilinear Algebra 60 (2012), 763-768 (pdf)
  27. Lie superautomorphisms on associative algebras, II, Algebras Repr. Th. 15 (2012), 507-525 (with Y. Bahturin and Š. Špenko) (pdf)
  28. Determining elements in Banach algebras through spectral properties, J. Math. Anal. Appl. 393 (2012), 144-150 (with Š. Špenko) (pdf)
  29. On Lie and associative algebras containing inner derivations, Linear Algebra Appl. 437 (2012), 648-658 (with Š. Špenko) (pdf)
  30. Maps preserving zeros of a polynomial, Linear Algebra Appl. 436 (2012), 2504-2512 (with J. Alaminos, Š. Špenko, and A. R. Villena) (pdf)
  31. A note on spectrum-preserving maps, J. Math. Anal. Appl. 387 (2012), 595-603 (with J. Alaminos, P. Šemrl, and A. R. Villena) (pdf)
  32. Tracial Nullstellensatze, in Notions of Positivity and the Geometry of Polynomials, Trends in Mathematics (2011), 79-101 (with I. Klep) (pdf)
  33. An alternative approach to the structure theory of PI-rings, Expo. Math. 29 (2011), 159-164 (pdf)
  34. Jordan gradings on associative algebras, Algebras Repr. Th. 14 (2011),113-129 (with Y. Bahturin and I. Shestakov) (pdf)
  35. On locally complex algebras and low-dimensional Cayley-Dickson algebras, J. Algebra 327 (2011), 107-125 (with P. Šemrl and Š. Špenko) (pdf)
  36. On a class of finitary Lie algebras characterized through derivations, Proc. Amer. Math. Soc. 138 (2010), 4161-4166 (with A. Fernandez Lopez) (pdf)
  37. 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)
  38. 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)
  39. Lie superautomorphisms on associative algebras, Proc. Amer. Math. Soc. 138 (2010), 417-425 (with Y. Bahturin) (pdf)
  40. 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)
  41. A note on values of noncommutative polynomials, Proc. Amer. Math. Soc. 138 (2010), 2375-2379 (with I. Klep) (pdf)
  42. An elementary approach to Wedderburn's structure theory, Expo. Math. 28 (2010), 79-83 (pdf)
  43. Values of noncommutative polynomials, Lie skew-ideals and tracial Nullstellensatze, Math. Res. Letters 16 (2009), 605-626 (with I. Klep) (pdf)
  44. 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)
  45. Maps preserving zero products, Studia Math. 193 (2009), 131-159 (with J. Alaminos, J. Extremera, and A. R. Villena) (pdf)
  46. Lie gradings on associative algebras, J. Algebra 321 (2009), 264-283 (with Y. Bahturin) (pdf)
  47. Polynomially compact derivations on Banach algebras, Stud. Math. 190 (2009), 185-191 (with Y. Turovskii) (pdf)
  48. Zero product determined matrix algebras, Linear Algebra Appl. 430 (2009), 1486-1498 (with M. Grašič and J. Sanchez) (pdf)
  49. Range-inclusive maps in rings with idempotents, Comm. Algebra 37 (2009), 154-163.
  50. When Jordan submodules are bimodules, Quart. J. Math. 59 (2008), 409-440 (with E. Kissin and V. Shulman) (pdf)
  51. Near-derivations in Lie algebras, J. Algebra 320 (2008), 3765-3772 (pdf)
  52. Lie ideals: from pure algebra to C*-algebras, J. Reine Angew. Math. 623 (2008), 73-121 (with E. Kissin and V. Shulman) (pdf)
  53. 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)
  54. Jordan homomorphisms revisited, Math. Proc. Camb. Phil. Soc. 144 (2008), 317-328 (pdf)
  55. An extension of the Gleason-Kahane-Zelazko theorem: a possible approach to Kaplansky's problem, Expo. Math. 26 (2008), 269-277 (with P. Šemrl).
  56. On Jordan ideals and submodules: algebraic and analytical aspects, Funct. Anal. Appl. 42 (2008), 220-223 (with E. Kissin and V. Shulman).
  57. Commutativity preserving maps revisited, Israel J. Math. 162 (2007), 317-334.
  58. Compactness conditions for elementary operators, Stud. Math. 178 (2007), 1-18 (with Y. Turovskii) (pdf)
  59. Characterizing homomorphisms, derivations and multipliers in rings with idempotents, Proc. Royal Soc. Edinb. Sect. A 137 (2007), 9-21 (pdf)
  60. 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).
  61. On bilinear maps on matrices with applications to commutativity preservers, J. Algebra 301 (2006), 803-837 (with P. Šemrl).
  62. On the multiplication ring of a prime ring, Comm. Algebra 34 (2006), 2195-2203 (with W. S. Martindale).
  63. 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).
  64. Jordan derivations revisited, Math. Proc. Camb. Phil. Soc. 139 (2005), 411-425 (pdf)
  65. The range and kernel inclusion of algebraic derivations and commuting maps, Quart. J. Math. 56 (2005), 31-41.
  66. Jordan ideals revisited, Monatsh. Math. 145 (2005), 1-10 (with A. Fošner and M. Fošner).
  67. Commutativity preserving linear maps on central simple algebras, J. Algebra 284 (2005), 102-110 (with P. Šemrl).
  68. Elementary operators as Lie homomorphisms or commutativity preservers, Proc. Edinb. Math. Soc. 48 (2005), 37-49 (with P. Šemrl).
  69. Commuting maps: A survey, Taiwan. J. Math. 8 (2004), 361-397.
  70. 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).
  71. On commutators and derivations in rings, J. Algebra 278 (2004), 704-724 (with D. Eremita and T.-L. Wong).
  72. 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).
  73. Commuting traces of biadditive maps revisited, Comm. Algebra 31 (2003), 381-388 (with P. Šemrl).
  74. A note on invertibility preservers on Banach algebras, Proc. Amer. Math. Soc. 131 (2003), 3833-3837 (with A. Fošner and P. Šemrl).
  75. Functional identities in Jordan algebras: Associating traces and Lie triple isomorphisms, Comm. Algebra 31 (2003), 1207-1234 (with D. Eremita and A. R. Villena).
  76. The lower socle and finite rank elementary operators, Comm. Algebra 31 (2003), 1485-1497 (with D. Eremita).
  77. On d-free rings, Comm. Algebra 31 (2003), 2287-2309.
  78. Jordan superhomomorphisms, Comm. Algebra 31 (2003), 633-644 (with K. I. Beidar and M. A. Chebotar) (pdf)
  79. The noncommutative Singer-Wermer conjecture and phi-derivations, J. London Math. Soc. 66 (2002), 710-720 (with A. R. Villena).
  80. On a certain functional identity in prime rings, II, Beitr. Alg. Geom. 43 (2002), 333-338 (with M. A. Chebotar).
  81. Functional identities in Jordan algebras: Associating maps, Comm. Algebra 30 (2002), 5241-5252 (with M. Cabrera and A. R. Villena).
  82. On automorphisms of Banach algebras, Arch. Math. 78 (2002), 297-302.
  83. 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).
  84. Functional identities with r-independent coefficients, Comm. Algebra 30 (2002), 5725-5755 (with K. I. Beidar and M. A. Chebotar).
  85. Functional identities revised: the fractional and the strong degree, Comm. Algebra 30 (2002), 935-969 (with K.I. Beidar and M. A. Chebotar).
  86. On Herstein's Lie map conjectures, III, J. Algebra 249 (2002), 59-94 (with K.I. Beidar, M. A. Chebotar, and W. S. Martindale).
  87. On Herstein's Lie map conjectures, II, J. Algebra 238 (2001), 239-264 (with K.I. Beidar, M. A. Chebotar, and W. S. Martindale).
  88. 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).
  89. A Kleinecke-Shirokov type condition with Jordan automorphisms, Studia Math. 147 (2001), 237-242 (with A. Fošner and M. Fošner).
  90. The range of a derivation on a Jordan-Banach algebra, Studia Math. 146 (2001), 177-200 (with A. R. Villena).
  91. 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).
  92. Extended Jacobson density theoremfor rings with derivations and automorphisms, Israel J. Math. 122 (2001), 317-346 (with K.I. Beidar).
  93. Functional identities: A survey, Contemporary Math. 259 (2000), 93-109 (pdf)
  94. Functional identities on upper triangular matrix algebras, J. Math. Sci. 102 (2000), 4557-4565 (with K.I. Beidar and M. A. Chebotar).
  95. Elementary operators, II, Acta Sci. Math. 66 (2000), 769-791 (with L. Molnar and P. Šemrl).
  96. 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).
  97. Applying the density theorem for derivations to range inclusion problems, Studia Math. 138 (2000), 93-100 (with K. I. Beidar).
  98. On rings with involution equipped with some new product, Publ. Math. Debrecen 57 (2000), 121-134 (with M. Fošner).
  99. 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).
  100. On derivations of prime rings, Comm. Algebra 27 (1999), 3129-3135 (with M.A. Chebotar and P. Šemrl).
  101. 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).
  102. On locally linearly dependent operators and derivations, Trans. Amer. Math. Soc. 351 (1999), 1257-1275 (with P. Šemrl).
  103. Elementary operators, Proc. Royal Soc. Edinburgh Sect. A 129 (1999), 1115-1135 (with P. Šemrl).
  104. Spectral characterization of idempotents and invertibility preserving linear maps, Expo. Math. 17 (1999), 185-192 (with P. Šemrl).
  105. On additive maps of prime rings, II, Publ. Math. Debrecen 54 (1999), 39-54 (with B. Hvala).
  106. On a certain functional identity in prime rings, Comm. Algebra 26 (1998), 3765-3781 (with M. A. Chebotar).
  107. Invertibility preserving maps preserve idempotents, Michigan J. Math. 45 (1998), 483-488 (with P. Šemrl).
  108. Dependent automorphisms in prime rings, Canad. Math. Bull. 41 (1998), 452-462 (with W. S. Martindale and C. R. Miers).
  109. Maps preserving nth powers, Comm. Algebra 26 (1998), 117-138 462 (with W. S. Martindale and C. R. Miers).
  110. Finite rank elements in semisimple Banach algebras, Studia Math. 128 (1998), 287-298 (with P. Šemrl).
  111. On certain pairs of automorphisms of rings, II, J. Austral. Math. Soc. 64 (1998), 162-168.
  112. Derivations mapping into the socle, II, Proc. Amer. Math. Soc. 126 (1998), 181-187.
  113. Linear preservers on B(X), Banach Center Publ. 38 (1997), 49-58 (with P. Šemrl).
  114. On a certain identity satisfied by a derivation and an arbitrary additive mapping II, Aequationes Math. 51 (1996), 83-85.
  115. Derivations mapping into the socle, Math. Proc. Camb. Phil. Soc. 120 (1996), 339-346 (with P. Šemrl).
  116. Spectral characterizations of central elements in Banach algebras, Studia Math. 120 (1996), 47-52 (with P. Šemrl).
  117. On local automorphisms and mappings that preserve idempotents, Studia Math. 113 (1995), 101-108 (with P. Šemrl).
  118. Linear maps preserving the spectral radius, J. Funct. Anal. 142 (1996), 360-368 (with P. Šemrl).
  119. Commuting maps on Lie ideals, Comm. Algebra 23 (1995), 5539-5553 (with C. R. Miers).
  120. Derivations mapping into the radical, III, J. Funct. Anal. 133 (1995), 21-29 (with M. Mathieu).
  121. On additive maps of prime rings, Bull. Austral. Math. Soc. 51 (1995), 377-381 (with B. Hvala).
  122. Applying the theorem on functional identities, Nova J. Math. Game Th. Alg. 4 (1995), 43-54.
  123. On generalized biderivations and related maps, J. Algebra 172 (1995), 764-786.
  124. Functional identities of degree two, J. Algebra 172 (1995), 690-720.
  125. Strong commutativity preserving maps of semiprime rings, Canad. Math. Bull. 37 (1994), 457-460 (with C. R. Miers).
  126. Derivations of noncommutative Banach algebras II, Arch. Math. 63 (1994), 56-59.
  127. One-sided ideals and derivations of prime rings, Proc. Amer. Math. Soc. 122 (1994), 979-983.
  128. Normal-preserving linear mappings, Canad. Math. Bull. 37 (1994), 306-309 (with P. Šemrl).
  129. On certain pairs of functions of semiprime rings, Proc. Amer. Math. Soc. 120 (1994), 709-713.
  130. 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}.
  131. On certain subrings of prime rings with derivations, J. Austral. Math. Soc. 54 (1993), 133-141 (with J. Vukman).
  132. Linear transformations preserving potent matrices, Proc. Amer. Math. Soc. 119 (1993), 81-86 (with P. Šemrl).
  133. Mappings which preserve idempotents, local automorphisms, and local derivations, Canad. J. Math. 45 (1993), 483-496 (with P. Šemrl).
  134. On some identities in prime rings with involution, Comm. Algebra 21 (1993), 4679-4697 (with W. S. Martindale and C. R. Miers).
  135. Commutativity preserving mappings of von Neumann algebras, Canad. J. Math. 45 (1993), 695-708 (with C. R. Miers).
  136. Centralizing maps in prime rings with involution, J. Algebra 161 (1993), 342-357 (with W. S. Martindale and C. R. Miers).
  137. Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings,Trans. Amer. Math. Soc. 335 (1993), 525-546.
  138. Derivations decreasing the spectral radius, Arch. Math. 61 (1993), 160-162.
  139. On skew-commuting mappings of rings, Bull. Austral. Math. Soc. 47 (1993), 291-296.
  140. Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), 385-394.
  141. On certain pairs of automorphisms of rings, J. Austral. Math. Soc. 54 (1993), 29-38.
  142. On the structure of Jordan *-derivations, Colloq. Math. 63 (1992), 163-171 (with B. Zalar).
  143. Derivations of noncommutative Banach algebras, Arch. Math. 59 (1992), 363-370 (with J. Vukman).
  144. On the compositions of (alpha,beta)-derivations of rings, and applications to von Neumann algebras, Acta. Sci. Math. 56 (1992), 369-375.
  145. Characterizations of derivations on some normed algebras with involution, J. Algebra 152 (1992), 454-462.
  146. On a generalization of the notion of centralizing mappings, Proc. Amer. Math. Soc. 114 (1992), 641-649.
  147. Jordan (theta, phi)-derivations, Glasnik Mat. 26 (1991), 13-17 (with J. Vukman).
  148. Jordan mappings of semiprime rings II, Bull. Austral. Math. Soc. 44 (1991), 233-238.
  149. Centralizing mappings on von Neumann algebras, Proc. Amer. Math. Soc. 111 (1991), 501-510.
  150. On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89-93.
  151. A note on derivations, Math. J. Okayama Univ. 32 (1990), 83-88.
  152. On left derivations and related mappings, Proc. Amer. Math. Soc. 110 (1990), 7-16 (with J. Vukman).
  153. Semiderivations of prime rings, Proc. Amer. Math. Soc. 108 (1990), 859-860.
  154. On some additive mappings in rings with involution, Aequationes Math. 38 (1989), 178-185 (with J. Vukman).
  155. Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228.
  156. Orthogonal derivations and an extension of a theorem of Posner, Rad. Mat. 5 (1989), 237-246 (with J. Vukman).
  157. Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006.
  158. Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-322 (with J. Vukman).