Strong commutativity preserving generalized derivations on Lie ideals

References

• Bai , Z , Du , S and Hou , J . 2008 . Multiplicative Lie isomorphisms between prime rings . Comm. Algebra , 36 : 1626 – 1633 .
   Web of Science ®Google Scholar
• Beidar , KI . 1978 . Rings of quotients of semiprime rings . Vestnik Moskov. Univ. Ser I Math. Meh. (Engl. Transl. Moscow Univ. Math. Bull.) , 33 : 36 – 42 .
   Google Scholar
• Beidar , KI and Lin , Y-F . 2004 . On surjective linear maps preserving commutativity . Proc. R. Soc. Edinb. Sec. A , 134 : 1023 – 1040 .
   Google Scholar
• Beidar , KI , Martindale 3rd , WS and Mikhalev , AV . 1996 . Rings with Generalized Identities , New York–Basel, , Hong Kong : Marcel Dekker, Inc. .
   Google Scholar
• Bell , HE and Daif , MN . 1994 . On commutativity and strong commutativity preserving maps . Canad. Math. Bull. , 37 : 443 – 447 .
   Web of Science ®Google Scholar
• Boudi , N and Ouchrif , S . 2009 . On generalized derivations in Banach algebras . Stud. Math. , 194 : 81 – 89 .
   Web of Science ®Google Scholar
• Brešar , M . 1991 . On the distance of the composition of two derivations to the generalized derivations . Glasg. Math. J. , 33 : 89 – 93 .
   Web of Science ®Google Scholar
• Brešar , M . 1993 . Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings . Trans. Am. Math. Soc. , 335 : 525 – 546 .
   Web of Science ®Google Scholar
• Brešar , M . 2007 . Commutativity preserving maps revisited . Israel J. Math. , 162 : 317 – 334 .
   Web of Science ®Google Scholar
• Brešar , M and Miers , CR . 1994 . Strong commutativity preserving maps of semiprime rings . Canad. Math. Bull. , 37 : 457 – 460 .
   Web of Science ®Google Scholar
• Brešar , M and Šemrl , P . 2005 . Commutativity preserving linear maps on central simple algebras . J. Algebra , 284 : 102 – 110 .
   Web of Science ®Google Scholar
• Brešar , M and Šemrl , P . 2006 . On bilinear maps on matrices with applications to commutativity preservers . J. Algebra , 301 : 803 – 837 .
   Web of Science ®Google Scholar
• Chebotar , MA , Ke , W-F and Lee , P-H . 2005 . On maps preserving zeros of the polynomial xy − yx* . Linear Algebra Appl. , 408 : 230 – 243 .
   Web of Science ®Google Scholar
• Cui , J and Hou , J . 2006 . Linear maps preserving elements annihilated by the polynomial XY − YX . Studia Math. , 174 : 183 – 199 .
   Web of Science ®Google Scholar
• De Filippis , V . 2007 . An Engel condition with generalized derivations on multilinear polynomials . Israel J. Math. , 162 : 93 – 108 .
   Web of Science ®Google Scholar
• De Filippis , V . 2009 . Generalized derivations with Engel condition on multilinear polynomials . Israel J. Math. , 171 : 325 – 348 .
   Web of Science ®Google Scholar
• Deng , Q and Ashraf , M . 1996 . On strong commutativity preserving maps . Results Math. , 30 : 259 – 263 .
   Google Scholar
• Dolinar , G . 2007 . Maps on upper triangular matrices preserving Lie products . Linear Multilinear Algebra , 55 : 191 – 198 .
   Web of Science ®Google Scholar
• Dolinar , G and Šemrl , P . 2004 . Maps on matrix algebras preserving commutativity . Linear Multilinear Algebra , 52 : 69 – 78 .
   Web of Science ®Google Scholar
• Fošner , M and Vukman , J . 2007 . On some equations in prime rings . Monatsh. Math. , 152 : 135 – 150 .
   Web of Science ®Google Scholar
• Han , D and Wei , F . 2010 . Generalized Jordan left derivations on semiprime algebras . Monatsh. Math. , 161 : 77 – 83 .
   Google Scholar
• Herstein , IN . 1969 . Topics in Ring Theory , Chicago : University of Chicago Press .
   Google Scholar
• Herstein , IN . 1976 . Rings with Involution , Chicago : University of Chicago Press .
   Google Scholar
• Hvala , B . 1998 . Generalized derivations in rings . Comm. Algebra , 26 : 1147 – 1166 .
   Web of Science ®Google Scholar
• Kharchenko , VK . 1979 . Differential identities of semiprime rings . Algebra Log. , 18 : 86 – 119 .
   Google Scholar
• Lanski , C . 2007 . Generalized derivations and nth power maps in rings . Comm. Algebra , 35 : 3660 – 3672 .
   Web of Science ®Google Scholar
• Lee , T-K . 1992 . Semiprime rings with differential identities . Bull. Inst. Math. Acad. Sin. , 20 : 27 – 38 .
   Google Scholar
• Lee , T-K . 1999 . Generalized derivations of left faithful rings . Comm. Algebra , 27 : 4057 – 4073 .
   Web of Science ®Google Scholar
• Lee , T-K . 1999 . Differential identities of Lie ideals or large right ideals in prime rings . Comm. Algebra , 27 : 793 – 810 .
   Web of Science ®Google Scholar
• Lee , T-K and Zhou , Y . 2009 . An identity with generalized derivations . J. Algebra Appl. , 8 : 307 – 317 .
   Web of Science ®Google Scholar
• Liao , P-B and Liu , C-K . 2009 . On generalized Lie derivations of Lie ideals of prime algebras . Linear Algebra Appl. , 430 : 1236 – 1242 .
   Web of Science ®Google Scholar
• Lin , J-S and Liu , C-K . 2006 . Generalized derivations with invertible or nilpotent values on multilinear polynomials . Comm. Algebra , 34 : 633 – 640 .
   Web of Science ®Google Scholar
• Lin , J-S and Liu , C-K . 2006 . Generalized derivations with nilpotent values on multilinear polynomials . Taiwanese J. Math. , 10 : 1183 – 1192 .
   Web of Science ®Google Scholar
• Lin , J-S and Liu , C-K . 2008 . Strong commutativity preserving maps on Lie ideals . Linear Algebra Appl. , 428 : 1601 – 1609 .
   Web of Science ®Google Scholar
• Lin , J-S and Liu , C-K . 2010 . Strong commutativity preserving maps in prime rings with involution . Linear Algebra Appl. , 432 : 14 – 23 .
   Web of Science ®Google Scholar
• Liu , C-K and Shiue , W-K . 2007 . Generalized Jordan triple (θ, φ)-derivations on semi-prime rings . Taiwanese J. Math. , 11 : 1397 – 1406 .
   Google Scholar
• Ma , F and Ji , G . 2007 . Generalized Jordan derivations on triangular matrix algebras . Linear Multilinear Algebra , 152 : 135 – 150 .
   Google Scholar
• Ma , J , Xu , XW and Niu , FW . 2008 . Strong commutativity preserving generalized derivations on semiprime rings . Acta Math. Sin. (Engl. Ser.) , 24 : 1835 – 1842 .
   Web of Science ®Google Scholar
• Martindale III , WS . 1969 . Prime rings satisfying a generalized polynomial identity . J. Algebra , 12 : 576 – 584 .
   Web of Science ®Google Scholar
• Molnár , L . 2009 . Linear maps on matrices preserving commutativity up to a factor . Linear Multilinear Algebra , 57 : 13 – 18 .
   Web of Science ®Google Scholar
• Qi , X and Hou , J . 2010 . Nonlinear strong commutativity preserving maps on prime rings . Comm. Algebra , 38 : 2790 – 2796 .
   Web of Science ®Google Scholar
• Radjavi , H and Šemrl , P . 2008 . Linear maps preserving quasi-commutativity . Stud. Math. , 184 : 191 – 204 .
   Web of Science ®Google Scholar
• Šemrl , P . 2008 . Commutativity preserving maps . Linear Algebra Appl. , 429 : 1051 – 1070 .
   Web of Science ®Google Scholar
• Watkins , W . 1976 . Linear maps that preserve commuting pairs of matrices . Linear Algebra Appl. , 14 : 29 – 35 .
   Web of Science ®Google Scholar
• Zhou , J , Wang , D and Zhang , Q . 2010 . Square-zero derivations of matrix algebras over commutative rings . Linear Multilinear Algebra , 58 : 239 – 243 .
   Web of Science ®Google Scholar