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Notes on generalized derivations on Lie ideals in prime rings

Basudeb Dhara|Vincenzo De Filippis
대한수학회 (The Korean Mathematical Society)|2009.05|대한수학회보 (Bulletin of the KMS)|제46권 제3호|pp. 599-605

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참고문헌

키워드

derivationgeneralized derivationprime ringUtumi quotient ringextended centroid
주제분류수학

초록

Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that u^sH(u)u^t=0 for all u ∈ L, where s≥ 0, t≥0 are fixed integers. Then H(x)=$ for all x∈ R unless char R=2 and R satisfies S_(4), the standard identity in four variables.

Abstract

Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that u^sH(u)u^t=0 for all u ∈ L, where s≥ 0, t≥0 are fixed integers. Then H(x)=$ for all x∈ R unless char R=2 and R satisfies S_(4), the standard identity in four variables.

참고문헌 (15)

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  8. B. Hvala, "Generalized derivations in rings", Comm. Algebra, 26(4), pp.1147~1166 (1998)
  9. N. Jacobson, "Structure of Rings", pp.37~ (1964), Math. Soc. Colloq. Pub
  10. V. K. Kharchenko, "Differential identities of prime rings", Algebra i Logika, 17(2), pp.220~243 (1978)
  11. C. Lanski, "Differential identities, Lie ideals, and Posner’s theorems", Pacific J. Math., 134(2), pp.275~297 (1988)
  12. C. Lanski, "An Engel condition with derivation", Proc. Amer. Math. Soc, 118(3), pp.731~734 (1993)
  13. T. K. Lee, "Generalized derivations of left faithful rings", Comm. Algebra, 27(8), pp.4057~4073 (1999)
  14. T. K. Lee, "Semiprime rings with differential identities", Bull. Inst. Math. Acad. Sinica, 20(1), pp.27~38 (1992)
  15. W. S. Martindale III, "Prime rings satisfying a generalized polynomial identity", J. Algebra, 12, pp.576~584 (1969)

관련 논문AI추천

Generalized derivations with annihilator conditions in prime ringsYu Wang대한수학회 · 대한수학회보2011 · 제48권 제5호Annihilating Conditions of Generalized Skew Derivations on Lie IdealsJunaid Nisar, Nadeem Ur Rehman, Sajad Ahmad Pary경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2023 · 제63권 제3호A NOTE ON SKEW DERIVATIONS IN PRIME RINGSAjda Fonsner, Vincenzo De Filippis대한수학회 · 대한수학회보2012 · 제49권 제4호NOTES ON (σ, τ)-DERIVATIONS OF LIE IDEALS IN PRIME RINGSOznur Golbasi, Seda Oguz대한수학회 · 대한수학회논문집2012 · 제27권 제3호Derivations with annihilator conditions in prime ringsBasudeb Dhara, Sachhidananda Mondal, Sukhendu Kar대한수학회 · 대한수학회보2013 · 제50권 제5호Generalized derivations on semiprime ringsVincenzo De Filippis대한수학회 · 대한수학회보2011 · 제48권 제6호

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