논문KCI 등재
Derivations with annihilator conditions in prime rings
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Let R be a prime ring, I a nonzero ideal of R, d a derivation of R, m(≥ 1), n(≥ 1) two fixed integers and a ∈ R. (i) If a((d(x)y + xd(y) + d(y)x + yd(x))n − (xy + yx))m = 0 for all x, y ∈ I, then either a = 0 or R is commutative; (ii) If char(R) 6≠2 and a((d(x)y + xd(y) + d(y)x +yd(x))n −(xy +yx)) ∈ Z(R) for all x, y ∈ I, then either a = 0 or R is commutative.
Abstract
Let R be a prime ring, I a nonzero ideal of R, d a derivation of R, m(≥ 1), n(≥ 1) two fixed integers and a ∈ R. (i) If a((d(x)y + xd(y) + d(y)x + yd(x))n − (xy + yx))m = 0 for all x, y ∈ I, then either a = 0 or R is commutative; (ii) If char(R) 6≠2 and a((d(x)y + xd(y) + d(y)x +yd(x))n −(xy +yx)) ∈ Z(R) for all x, y ∈ I, then either a = 0 or R is commutative.
참고문헌 (15)
- Nurcan Argac, "Derivations of prime and semiprime rings", 대한수학회지, 46(5), pp.997~1005 (2009), 대한수학회
- M. Ashraf, "On commutativity of rings with derivations", Results Math, 42(1), pp.3~8 (2002)
- L. Carini, "Annihilators on co-commutators with general- ized derivations on Lie ideals", Publ. Math. Debrecen, 76(3), pp.395~409 (2010)
- C. M. Chang, "Annihilators of power values of derivations in prime rings", Comm. Algebra, 26(7), pp.2091~2113 (1998)
- C. L. Chuang, "GPI’s having coefficients in Utumi quotient rings", Proc. Amer. Math. Soc, 103(3), pp.723~728 (1988)
- V. De Filippis, "Lie ideals and annihilator conditions on power values of commutators with derivation", Indian J. Pure Appl. Math, 32(5), pp.649~656 (2001)
- B. Dhara, "Power values of derivations with annihilator conditions on Lie ideals in prime rings", Comm. Algebra, 37(6), pp.2159~2167 (2009)
- B. Dhara, "Annihilator condition on power values of derivations", Indian J. Pure Appl. Math, 42(5), pp.357~369 (2011)
- B. Dhara, "Left annihilators of power values of commutators with generalized derivations", Georgian Math. J, 19(3), pp.441~448 (2012)
- T. S. Erickson, "Prime nonassociative algebras", Pacific J. Math, 60(1), pp.49~63 (1975)
- I. N. Herstein, "Topics in Ring Theory" (1969), Univ. of Chicago Press
- V. K. Kharchenko, "Differantial identities of prime rings", Algebra i Logika, 17(2), pp.220~238 (1978)
- C. Lanski, "An Engel condition with derivation", Proc. Amer. Math. Soc, 118(3), pp.731~734 (1993)
- W. S.Martindale III, "Prime rings satisfying a generalized polynomial identity", J. Algebra, 12, pp.576~584 (1969)
- E. C. Posner, "Derivations in prime rings", Proc. Amer. Math. Soc, 8, pp.1093~1100 (1957)
관련 논문AI추천
Derivations of prime and semiprime ringsHulya G. Inceboz, Nurcan Argac대한수학회 · 대한수학회지2009 · 제46권 제5호Generalized derivations on semiprime ringsVincenzo De Filippis대한수학회 · 대한수학회보2011 · 제48권 제6호Generalized derivations with centralizing conditions in prime ringsBasudeb Dhara, Priyadwip Das, Sukhendu Kar대한수학회 · 대한수학회논문집2019 · 제34권 제1호Generalized 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 제3호Notes on generalized derivations on Lie ideals in prime ringsBasudeb Dhara, Vincenzo De Filippis대한수학회 · 대한수학회보2009 · 제46권 제3호
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