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GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS

Yıl 2014, Cilt: 43 Sayı: 1, 69 - 83, 01.01.2014

Öz

Let R be a prime ring, f (x, . . . , xn ) a multilinear polynomial over Cin n noncommuting indeterminates, I a nonzero right ideal of R, andF : R → R be a nonzero generalized skew derivation of R.Suppose that F (f (r, . . . , rn ))f (r, . . . , rn ) ∈ C, for all r, . . . , rn ∈ I.If f (x, . . . , xn ) is not central valued on R, then either char(R) = 2and R satisfies sor one of the following holds:(i ) f (x, . . . , xn )x n+1 is an identity for I;(ii ) F (I)I = (0);(iii ) [f (x, . . . , xn ), x n+1 ]x n+2 is an identity for I, there existb, c, q ∈ Q with q an invertible element such that F (x) =bx − qxq−1 c for all x ∈ R, and q−1 cI ⊆ I.Moreover, inthis case either (b − c)I = (0) or b − c ∈ C and f (x, . . . , xn ) is central valued on R.

Kaynakça

  • C ¸ . Demir, N. Arga¸ c, Prime rings with generalized derivations on right ideals, Algebra Colloq. 18 (Spec. 1), 987-998, 2011.
  • K.I. Beidar, W.S. Martindale, III, A.V. Mikhalev, Rings with generalized identities(Monographs and Textbooks in Pure and Applied Mathematics, 196, 1996).
  • M. Bresar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (2), 385394, 1993.
  • M. Bresar, One-sided ideals and derivations of prime rings, Proc. Amer. Math. Soc. 122 (4), 979-983, 1994.
  • L. Carini, V. De Filippis, Identities with generalized derivations on prime rings and Banach algebras, Algebra Colloq., 19 (Spec. 1), 971-986, 2012.
  • C.M. Chang, Power central values of derivations on multilinear polynomials, Taiwanese J. Math. 7 (2), 329-338, 2003.
  • C.M. Chang, T.K. Lee, Annihilators of power values of derivations in prime rings, Comm. in Algebra 26 (7), 2091-2113, 1998.
  • J.C. Chang, On the identitity h(x) = af (x) + g(x)b, Taiwanese J. Math. 7 (1), 103-113, 2003. J. C. Chang, Generalized skew derivations with annihilating Engel conditions, Taiwanese J. Math. 12 (7), 1641-1650, 2008.
  • J. C. Chang, Generalized skew derivations with nilpotent values on Lie ideals, Monatsh. Math. 161 (2), 155-160, 2010.
  • H. W. Cheng and F. Wei, Generalized skew derivations of rings, Adv. Math. (China), 35 (2), 237-243, 2006.
  • C.L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (3), 723-728, 1988.
  • C.L. Chuang, Differential identities with automorphisms and antiautomorphisms I, J. Algebra 149 (2), 371-404, 1992.
  • C.L. Chuang, Differential identities with automorphisms and antiautomorphisms II, J. Algebra 160 (1), 130-171, 1993.
  • C.L. Chuang, T.K. Lee, Identities with a single skew derivation, J. Algebra 288 (1), 59-77, 200 C.L. Chuang, T.K. Lee, Rings with annihilator conditions on multilinear polynomials, Chinese J. Math. 24 (2), 177-185, 1996.
  • M.C. Chou, C.K. Liu, An Engel condition with skew derivations, Monatsh. Math. 158 (3), 259-270, 2009.
  • V. De Filippis, F. Wei, Posner’s second theorem for skew derivations on left ideals, Houston J. Math. 38 (2), 373-395, 2012.
  • C. Faith, Y. Utumi, On a new proof of Litoff ’s Theorem, Acta Math. Acad. Sci. Hungar 14, 369-371, 1963.
  • N. Jacobson, Structure of rings (American Mathematical Society Colloquium Publications, Vol. Revised edition American Mathematical Society, Providence, R.I. 1964).
  • V.K. Kharchenko, Generalized identities with automorphisms, Algebra and Logic 14 (2), 132-148, 1975.
  • C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc. 118 (3), 731-734, 19 T.K. Lee, Derivations with invertible values on a multilinear polynomial, Proc. Amer. Math. Soc. 119 (4), 1077-1083, 1993.
  • T.K. Lee, Left annihilators characterized by GPIs, Trans. Amer. Math. Soc. 347 (8), 31593165, 1995.
  • T.K. Lee, Power reduction property for generalized identities of one-sided ideals, Algebra Colloq. 3 (1), 19-24, 1996.
  • T.K. Lee, Generalized skew derivations characterized by acting on zero products, Pacific J. Math. 216 (2), 293-301, 2004.
  • T.K. Lee, W.K. Shiue Derivations cocentralizing polynomials, Taiwanese J. Math. 2 (4), 457-467, 1998.
  • T.K. Lee, Y. Zhou, An identity with generalized derivations, J. Algebra and Appl. 8 (3), 307-317, 2009.
  • P.H. Lee, T.L. Wong, Derivations cocentralizing Lie ideals, Bull. Inst. Math. Acad. Sinica 23 (1), 1-5, 1995.
  • U. Leron, Nil and power central polynomials in rings, Trans. Amer. Math. Soc. 202, 97-103, 19 W.S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12, 576-584, 1969.
  • E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8, 1093-1100, 1957.
  • T.L. Wong, Derivations with power central values on multilinear polynomials, Algebra Colloq. 3 (4), 369-378, 1996.

GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS

Yıl 2014, Cilt: 43 Sayı: 1, 69 - 83, 01.01.2014

Öz

-

Kaynakça

  • C ¸ . Demir, N. Arga¸ c, Prime rings with generalized derivations on right ideals, Algebra Colloq. 18 (Spec. 1), 987-998, 2011.
  • K.I. Beidar, W.S. Martindale, III, A.V. Mikhalev, Rings with generalized identities(Monographs and Textbooks in Pure and Applied Mathematics, 196, 1996).
  • M. Bresar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (2), 385394, 1993.
  • M. Bresar, One-sided ideals and derivations of prime rings, Proc. Amer. Math. Soc. 122 (4), 979-983, 1994.
  • L. Carini, V. De Filippis, Identities with generalized derivations on prime rings and Banach algebras, Algebra Colloq., 19 (Spec. 1), 971-986, 2012.
  • C.M. Chang, Power central values of derivations on multilinear polynomials, Taiwanese J. Math. 7 (2), 329-338, 2003.
  • C.M. Chang, T.K. Lee, Annihilators of power values of derivations in prime rings, Comm. in Algebra 26 (7), 2091-2113, 1998.
  • J.C. Chang, On the identitity h(x) = af (x) + g(x)b, Taiwanese J. Math. 7 (1), 103-113, 2003. J. C. Chang, Generalized skew derivations with annihilating Engel conditions, Taiwanese J. Math. 12 (7), 1641-1650, 2008.
  • J. C. Chang, Generalized skew derivations with nilpotent values on Lie ideals, Monatsh. Math. 161 (2), 155-160, 2010.
  • H. W. Cheng and F. Wei, Generalized skew derivations of rings, Adv. Math. (China), 35 (2), 237-243, 2006.
  • C.L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (3), 723-728, 1988.
  • C.L. Chuang, Differential identities with automorphisms and antiautomorphisms I, J. Algebra 149 (2), 371-404, 1992.
  • C.L. Chuang, Differential identities with automorphisms and antiautomorphisms II, J. Algebra 160 (1), 130-171, 1993.
  • C.L. Chuang, T.K. Lee, Identities with a single skew derivation, J. Algebra 288 (1), 59-77, 200 C.L. Chuang, T.K. Lee, Rings with annihilator conditions on multilinear polynomials, Chinese J. Math. 24 (2), 177-185, 1996.
  • M.C. Chou, C.K. Liu, An Engel condition with skew derivations, Monatsh. Math. 158 (3), 259-270, 2009.
  • V. De Filippis, F. Wei, Posner’s second theorem for skew derivations on left ideals, Houston J. Math. 38 (2), 373-395, 2012.
  • C. Faith, Y. Utumi, On a new proof of Litoff ’s Theorem, Acta Math. Acad. Sci. Hungar 14, 369-371, 1963.
  • N. Jacobson, Structure of rings (American Mathematical Society Colloquium Publications, Vol. Revised edition American Mathematical Society, Providence, R.I. 1964).
  • V.K. Kharchenko, Generalized identities with automorphisms, Algebra and Logic 14 (2), 132-148, 1975.
  • C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc. 118 (3), 731-734, 19 T.K. Lee, Derivations with invertible values on a multilinear polynomial, Proc. Amer. Math. Soc. 119 (4), 1077-1083, 1993.
  • T.K. Lee, Left annihilators characterized by GPIs, Trans. Amer. Math. Soc. 347 (8), 31593165, 1995.
  • T.K. Lee, Power reduction property for generalized identities of one-sided ideals, Algebra Colloq. 3 (1), 19-24, 1996.
  • T.K. Lee, Generalized skew derivations characterized by acting on zero products, Pacific J. Math. 216 (2), 293-301, 2004.
  • T.K. Lee, W.K. Shiue Derivations cocentralizing polynomials, Taiwanese J. Math. 2 (4), 457-467, 1998.
  • T.K. Lee, Y. Zhou, An identity with generalized derivations, J. Algebra and Appl. 8 (3), 307-317, 2009.
  • P.H. Lee, T.L. Wong, Derivations cocentralizing Lie ideals, Bull. Inst. Math. Acad. Sinica 23 (1), 1-5, 1995.
  • U. Leron, Nil and power central polynomials in rings, Trans. Amer. Math. Soc. 202, 97-103, 19 W.S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12, 576-584, 1969.
  • E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8, 1093-1100, 1957.
  • T.L. Wong, Derivations with power central values on multilinear polynomials, Algebra Colloq. 3 (4), 369-378, 1996.
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Matematik
Yazarlar

E. Albaş Bu kişi benim

N. Argaç Bu kişi benim

V. De Filippis Bu kişi benim

Ç. Demir Bu kişi benim

Yayımlanma Tarihi 1 Ocak 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 43 Sayı: 1

Kaynak Göster

APA Albaş, E., Argaç, N., Filippis, V. D., Demir, Ç. (2014). GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS. Hacettepe Journal of Mathematics and Statistics, 43(1), 69-83.
AMA Albaş E, Argaç N, Filippis VD, Demir Ç. GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS. Hacettepe Journal of Mathematics and Statistics. Ocak 2014;43(1):69-83.
Chicago Albaş, E., N. Argaç, V. De Filippis, ve Ç. Demir. “GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS”. Hacettepe Journal of Mathematics and Statistics 43, sy. 1 (Ocak 2014): 69-83.
EndNote Albaş E, Argaç N, Filippis VD, Demir Ç (01 Ocak 2014) GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS. Hacettepe Journal of Mathematics and Statistics 43 1 69–83.
IEEE E. Albaş, N. Argaç, V. D. Filippis, ve Ç. Demir, “GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS”, Hacettepe Journal of Mathematics and Statistics, c. 43, sy. 1, ss. 69–83, 2014.
ISNAD Albaş, E. vd. “GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS”. Hacettepe Journal of Mathematics and Statistics 43/1 (Ocak 2014), 69-83.
JAMA Albaş E, Argaç N, Filippis VD, Demir Ç. GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS. Hacettepe Journal of Mathematics and Statistics. 2014;43:69–83.
MLA Albaş, E. vd. “GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS”. Hacettepe Journal of Mathematics and Statistics, c. 43, sy. 1, 2014, ss. 69-83.
Vancouver Albaş E, Argaç N, Filippis VD, Demir Ç. GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS. Hacettepe Journal of Mathematics and Statistics. 2014;43(1):69-83.