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On permuting n-derivations in near-rings

Mohammad Aslam Siddeeque|Mohammad Ashraf
대한수학회 (The Korean Mathematical Society)|2013.10|대한수학회논문집 (Communications of the KMS)|제28권 제4호|pp. 697-707

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키워드

derivationsleft near-ringszero symmetricpermuting n-derivations
주제분류수학

초록

In this paper, we introduce the notion of permuting n-derivationsin near-ring N and investigate commutativity of addition andmultiplication of N. Further, under certain constrants on a n!-torsionfree prime near-ring N, it is shown that a permuting n-additive mappingD on N is zero if the trace d of D is zero. Finally, some more relatedresults are also obtained.

Abstract

In this paper, we introduce the notion of permuting n-derivationsin near-ring N and investigate commutativity of addition andmultiplication of N. Further, under certain constrants on a n!-torsionfree prime near-ring N, it is shown that a permuting n-additive mappingD on N is zero if the trace d of D is zero. Finally, some more relatedresults are also obtained.

참고문헌 (10)

  1. K. I. Beidar, "Posner and Herstein theorems for derivations of 3-prime near-rings", Comm. Algebra, 24(5), pp.1581~1589 (1996)
  2. H. E. Bell, "On derivations in near-rings. II, Nearrings, nearfields and K-loops (Hamburg, 1995)", Math. Appl, 426, pp.191~197 (1997)
  3. H. E. Bell, "On derivations in near-rings, Near-rings and near-fields (T¨ubingen, 1985)", North-Holland Math. Stud, 137, pp.31~35 (1987)
  4. G. Maksa, "A remark on symmetric biadditive functions having nonnegative diagonal- ization", Glas. Mat. Ser. III, 15(2), pp.279~282 (1980)
  5. G. Maksa, "On the trace of symmetric bi-derivations", C. R. Math. Rep. Acad. Sci. Canada, 9(6), pp.303~307 (1987)
  6. M. A. ¨Ozt¨urk, "Permuting tri-derivations in prime and semi prime rings", East. Asian. Math. J, 15(2), pp.177~190 (1999)
  7. M. A. ¨Ozt¨urk, "On trace of symmetric bi-derivations in near-rings", Int. J. Pure Appl. Math, 17(1), pp.95~102 (2004)
  8. Kyoo-Hong Park, "ON PRIME AND SEMIPRIME RINGS WITH SYMMETRIC n-DERIVATIONS", 충청수학회지, 22(3), pp.451~458 (2009), 충청수학회
  9. 박규홍, "ON PERMUTING 3-DERIVATIONS AND COMMUTATIVITY IN PRIME NEAR-RINGS", 대한수학회논문집, 25(1), pp.1~9 (2010), 대한수학회
  10. G. Pilz, "Near-rings", pp.1983, North Holland

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ON PERMUTING 3-DERIVATIONS AND COMMUTATIVITY IN PRIME NEAR-RINGS박규홍, 정용수대한수학회 · 대한수학회논문집2010 · 제25권 제1호Study of quotient near-rings with additive mapsAbdelilah Zerbane, Abdelkarim Boua, Abderrahmane Raji대한수학회 · 대한수학회논문집2024 · 제39권 제2호On semiderivations in $3$-prime near-ringsAbdelkarim Boua, Mohammad Ashraf대한수학회 · 대한수학회논문집2016 · 제31권 제3호On Skew Centralizing Traces of Permuting n-Additive MappingsMohammad Ashraf, Nazia Parveen경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제1호Structure of $3$-prime near-rings satisfying some identitiesAbdelkarim Boua대한수학회 · 대한수학회논문집2019 · 제34권 제1호Commutativity of Jordan ideals in 3-prime near-rings with derivationsAbdelkarim Boua대한수학회 · 대한수학회논문집2018 · 제33권 제1호

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