FUNCTIONAL IDENTITIES REVISED: THE FRACTIONAL AND THE STRONG DEGREE

REFERENCES

• Ara , P. and Mathieu , M. 1993 . An Application of Local Multipliers to Centralizing Mappings of C *-algebras . Quart. J. Math. Oxford , 44 : 129 – 138 .
   Web of Science ®Google Scholar
• Banning , R. and Mathieu , M. 1997 . Commutativity Preserving Mappings on Semiprime Rings . Comm. Algebra , 25 : 247 – 265 .
   Web of Science ®Google Scholar
• Baxter , W.E. and Martindale , W.S. 1979 . 3rd, Jordan Homomorphisms of Semiprime Rings . J. Algebra , 56 : 457 – 471 .
   Web of Science ®Google Scholar
• Beasley , L.B. 1978 . Linear Transformations on Matrices: The Invariance of Commuting Pairs of Matrices . Linear and Multilinear Algebra , 6 : 179 – 183 .
   Google Scholar
• Beidar , K.I. 1998 . On Functional Identities and Commuting Additive Mappings . Comm. Algebra , 26 : 1819 – 1850 .
   Web of Science ®Google Scholar
• Beidar , K.I. , Bre[sbreve]ar , M. and Chebotar , M.A. 1999 . Generalized Functional Identities with (Anti)automorphisms and Derivations on Prime Rings . I.J. Algebra , 215 : 644 – 665 .
   Web of Science ®Google Scholar
• Beidar , K.I. , Bre[sbreve]ar , M. and Chebotar , M.A. 2000 . Functional Identities on Upper Triangular Matrix Algebras . J. Math. Sci. , 102 : 4557 – 4565 .
   Google Scholar
• Beidar , K.I. , Bre[sbreve]ar , M. , Chebotar , M.A. and Martindale , W.S. 2000 . On Functional Identities in Prime Rings with Involution, II . Comm. Algebra , 28 : 3169 – 3183 . 3rd
   Web of Science ®Google Scholar
• Beidar , K.I. , Brešar , M. , Chebotar , M.A. and Martindale , W.S. On Herstein's Lie Map Conjectures . I. Trans. Amer. Math. Soc. , 3rd to appear
   Web of Science ®Google Scholar
• Beidar , K.I. , Bre[sbreve]ar , M. , Chebotar , M.A. and Martindale , W.S. On Herstein's Lie Map Conjectures, II . J. Algebra , 3rd to appear
   Web of Science ®Google Scholar
• Beidar , K.I. , Chang , S.-C. , Chebotar , M.A. and Fong , Y. 2000 . On Functional Identities in Left Ideals of Prime Rings . Comm. Algebra , 28 : 3041 – 3058 .
   Web of Science ®Google Scholar
• Beidar , K.I. and Chebotar , M.A. 2000 . On Functional Identities and d-free Subsets of Rings II . Comm. Algebra , 28 : 3925 – 3952 .
   Web of Science ®Google Scholar
• Beidar , K.I. and Chebotar , M.A. 2000 . On Functional Identities and d-free Subsets of Rings II . Comm. Algebra , 28 : 3953 – 3972 .
   Web of Science ®Google Scholar
• Beidar , K.I. and Chebotar , M.A. Lie Derivations of Lie Ideals of Prime Rings . Israel J. Math. , to appear
   Google Scholar
• Beidar , K.I. and Chebotar , M.A. 2000 . On Surjective Lie Homomorphisms onto Lie Ideals of Prime Rings . Comm. Algebra , 29 : 4775 – 4793 .
   Web of Science ®Google Scholar
• Beidar , K.I. and Chebotar , M.A. On Additive Maps onto Lie Ideals of Prime Rings Preserving a Polynomial . submitted
   Google Scholar
• Beidar , K.I. and Chebotar , M.A. 2000 . On Lie-admissible Algebras whose Commutator Lie Algebras are Lie Subalgebras of Prime Associative Algebras . J. Algebra , 233 : 675 – 703 .
   Web of Science ®Google Scholar
• Beidar , K.I. and Fong , Y. 1999 . On Additive Isomorphisms of Prime Rings Preserving Polynomials . J. Algebra , 217 : 650 – 667 .
   Web of Science ®Google Scholar
• Beidar , K.I. , Fong , Y. , Lee , P.-H. and Wong , T.-L. 1997 . On Additive Maps of Prime Rings Satisfying Engel Condition . Comm. Algebra , 25 : 3889 – 3902 .
   Web of Science ®Google Scholar
• Beidar , K.I. and Martindale , W.S. 1998 . On Functional Identities in Prime Rings with Involution . J. Algebra , 203 : 491 – 532 . 3rd
   Web of Science ®Google Scholar
• Beidar , K.I. , Martindale , W.S. and Mikhalev , A.V. 1994 . Lie Isomorphisms in Prime Rings with Involution . J. Algebra , 169 : 304 – 327 . 3rd
   Web of Science ®Google Scholar
• Beidar , K.I. , Martindale , W.S. and Mikhalev , A.V. 1996 . Rings with Generalized Identities New York : Marcel Dekker, Inc. . 3rd
   Google Scholar
• Blau , P.S. 1999 . Lie Isomorphisms of Non-GPI Rings with Involution . Comm. Algebra , 27 : 2345 – 2373 .
   Web of Science ®Google Scholar
• Berberian , S.K. 1972 . Baer *-rings New York, Berlin : Springer-Verlag .
   Google Scholar
• Bre[sbreve]ar , M. 1989 . Jordan Mappings of Semiprime Rings . J Algebra , 127 : 218 – 228 .
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. 1993 . Centralizing Mappings and Derivations in Prime Rings . J. Algebra , 156 : 385 – 394 .
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. 1993 . On Skew-commuting Mappings of Rings . Bull. Austral. Math. Soc. , 47 : 291 – 296 .
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. 1993 . Commuting Traces of Biadditive Mappings, Commutativity Preserving Mappings, and Lie Mappings . Trans. Amer. Math. Soc. , 335 : 525 – 546 .
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. 1995 . Functional Identities of Degree Two . J. Algebra , 172 : 690 – 720 .
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. 1995 . On Generalized Biderivations and Related Maps . J. Algebra , 172 : 764 – 786 .
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. 1995 . Applying the Theorem on Functional Identities . Nova J. Math., Game Theory, and Algebra , 4 : 43 – 54 .
   Google Scholar
• Bre[sbreve]ar , M. 1996 . On Certain Identity Satisfied by a Derivation and an Arbitrary Additive Map, II . Aequationes Math. , 51 : 83 – 85 .
   Google Scholar
• Bre[sbreve]ar , M. and Hvala , B. 1995 . On Additive Maps of Prime Rings . Bull. Austral. Math. Soc. , 51 : 377 – 381 .
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. 2000 . Functional Identities: A Survey . Contemporary Math. , 259 : 93 – 109 .
   Google Scholar
• Bre[sbreve]ar , M. and Chebotar , M.A. 1998 . On a Certain Functional Identity in Prime Rings . Comm. Algebra , 26 : 3765 – 3782 .
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. , Martindale , W.S. and Miers , C.R. 1998 . Maps Preserving nth Powers . Comm. Algebra , 26 : 117 – 138 . 3rd
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. , Martindale , W.S. and Miers , C.R. 1993 . Centralizing Maps in Prime Rings with Involution . J. Algebra , 161 : 342 – 357 . 3rd
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. and Miers , C.R. 1993 . Commutativity Preserving Mappings of von Neumann Algebras . Canad. J. Math. , 45 : 695 – 708 .
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. and Miers , C.R. 1994 . Strong Commutativity Preserving Maps of Semiprime Rings . Canad. Math. Bull. , 37 : 457 – 460 .
   Web of Science ®Google Scholar
• Bre[sbreve]ar , M. and Miers , C.R. 1995 . Commuting Maps on Lie Ideals . Comm. Algebra , 23 : 5339 – 5553 .
   Web of Science ®Google Scholar
• Chebotar , M.A. 1996 . On Lie Automorphisms of Simple Rings of Characteristic 2 . Fundamentalnaya i Prikladnaya Matematika , 2 : 1257 – 1268 . (Russian)
   Google Scholar
• Chebotar , M.A. 1998 . On Generalized Functional Identities in Prime Rings . J. Algebra , 202 : 655 – 670 .
   Web of Science ®Google Scholar
• Chebotar , M.A. 1999 . On Lie Isomorphisms in Prime Rings with Involution . Comm. Algebra , 27 : 2767 – 2777 .
   Web of Science ®Google Scholar
• Choi , M.D. , Jafarian , A.A. and Radjavi , H. 1987 . Linear Maps Preserving Commutativity . Linear Algebra Appl. , 87 : 227 – 242 .
   Web of Science ®Google Scholar
• Goodearl , K.R. 1979 . Von Neumann Regular Rings Pitman Publ. Inc. .
   Google Scholar
• Herstein , I.N. 1961 . Lie and Jordan Structures in Simple, Associative Rings . Bull. Amer. Math. Soc. , 67 : 517 – 531 .
   Web of Science ®Google Scholar
• Herstein , I.N. 1969 . Topics in Ring Theory The University of Chicago Press .
   Google Scholar
• Jacobson , N. 1956 . Structure of Rings Vol. 37 , Colloq. Publ. .
   Google Scholar
• Lagutina , L.A. 1998 . Jordan Homomorphisms of Associative Algebras with Involution . Algebra and Logic , 27 : 250 – 260 .
   Google Scholar
• Lanski , C. 1988 . Differential Identities, Lie Ideals, and Posner's Theorems . Pacif. J. Math. , 134 : 275 – 297 .
   Web of Science ®Google Scholar
• Lanski , C. 1997 . An Engel Condition with Derivation for Left Ideals . Proc. Amer. Math. Soc. , 125 : 339 – 345 .
   Web of Science ®Google Scholar
• Lee , P.-H. and Lee , T.-K. 1997 . Linear Identities and Commuting Maps in Rings with Involution . Comm. Algebra , 25 : 2881 – 2895 .
   Web of Science ®Google Scholar
• Lee , P.-H. , Wong , T.-L. , Lin , J.-S. and Wang , R.-J. 1997 . Commuting Traces of Multiadditive Mappings . J. Algebra , 193 : 709 – 723 .
   Web of Science ®Google Scholar
• Lee , T.-K. and Lee , T.-C. 1996 . Commuting Additive Mappings in Semiprime Rings . Bull. Inst. Math. Acad. Sinica , 24 : 259 – 268 .
   Google Scholar
• Lee , T.-K. σ-centralizing Mappings in Semiprime Rings . Comm. Algebra , to appear
   Google Scholar
• Magajna , B. 1993 . A Transitivity Theorem for Algebras of Elementary Operators . Proc. Amer. Math. Soc. , 118 : 119 – 127 .
   Web of Science ®Google Scholar
• Martindale , W.S. 1982 . Lie and Jordan Mappings . Contemp. Math. , 13 : 173 – 177 .
   Google Scholar
• Martindale , W.S. 1990 . Jordan Homomorphisms onto Nondegenerate Jordan Algebras . J. Algebra , 133 : 500 – 511 . 3rd
   Web of Science ®Google Scholar
• McCrimmon , K. 1989 . The Zelmanov Approach to Jordan Homomorphisms of Associative Algebras . J. Algebra , 123 : 457 – 477 .
   Web of Science ®Google Scholar
• Miers , C.R. 1988 . Commutativity Preserving Maps of Factors . Can. J. Math. , 40 : 248 – 256 .
   Web of Science ®Google Scholar
• Omladi[cbreve] , M. 1986 . On Operators Preserving Commutativity . J. Funct. Anal. , 66 : 105 – 122 .
   Web of Science ®Google Scholar
• Pierce , S. and Watkins , W. 1978 . Invariants of Linear Maps on Matrix Algebras . Linear and Multilinear Algebra , 6 : 185 – 200 .
   Google Scholar
• Procesi , C. 1973 . Rings with Polynomial Identities New-York : Marcel Dekker, Inc. .
   Google Scholar
• Rowen , L.H. 1980 . Polynomial Identities in Ring Theory Academic Press .
   Google Scholar
• Scholz , E. and Timmermann , W. 1993 . Local Derivations, Automorphisms and Commutativity Preserving Maps on L (+) (D) . Publ. Res. Inst. Math. Sci. , 29 : 977 – 995 .
   Web of Science ®Google Scholar
• Skosyrskii , V.G. 1989 . Strongly Prime Noncommutative Jordan Algebras . Trudy Inst. Mat. (Novosibirsk) , 16 : 131 – 164 . (Russian)
   Google Scholar
• Swain , G.A. 1996 . Lie Derivations of the Skew Elements of Prime Rings with Involution . J. Algebra , 184 : 679 – 704 .
   Web of Science ®Google Scholar
• Swain , G.A. and Blau , P.S. 1999 . Lie Derivations in Prime Rings with Involution . Canad. Math. Bull. , 42 : 401 – 411 .
   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
• Zelmanov , E.I. 1983 . Prime Jordan Algebras II . Siberian J. Math. , 24 : 89 – 104 .
   Web of Science ®Google Scholar