Kyungpook Mathematical Journal

  • 제61권4호
  • /
  • Pages.727-735
  • /
  • 2021
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

Identities in a Prime Ideal of a Ring Involving Generalized Derivations

  • 투고 : 2021.04.07
  • 심사 : 2021.10.06
  • 발행 : 2021.12.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we will study the structure of the quotient ring R/P of an arbitrary ring R by a prime ideal P. We do so using differential identities involving generalized derivations of R. We enrich our results with examples that show the necessity of their assumptions.

키워드

과제정보

The authors are greatly indebted to the referee for his/her constructive comments and suggestion, which improves the quality of the paper.

참고문헌

  1. L. K. Ardakani, B. Davvaz and S. Huang, On derivations of prime and semi-prime Gamma rings, Bol. Soc. Param. Mat., 37(2)(2019), 155-164.
  2. H. E. Bell and L. C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta. Math. Hungar., 53(1989), 339-346. https://doi.org/10.1007/BF01953371
  3. B. Davvaz and M. A. Raza, A note on automorphisms of Lie ideals in prime rings, Math. Slovaca, 68(5)(2018), 1223-1229. https://doi.org/10.1515/ms-2017-0179
  4. A. Mamouni, L. Oukhtite and M. Zerra, On derivations involving prime ideals and commutativity in rings, Sao Paulo J. Math. Sci., 14(2020), 675-688. https://doi.org/10.1007/s40863-020-00187-z
  5. H. E. Mir, A. Mamouni and L. Oukhtite, Commutativity with algebraic identities involving prime ideals, Commun. Korean Math. Soc., 35(3)(2020), 723-731. https://doi.org/10.4134/CKMS.C190338
  6. N. Rehman, On generalized derivations as homomorphisms and anti-homomorphisms, Glas. Mat., 39(59)(2004), 27-30. https://doi.org/10.3336/gm.39.1.03
  7. N. Rehman, F. Alsarari and H. AlNoghashi, Action of prime ideals on generalized derivations-I, Preprint.
  8. G. S. Sandhu and B. Davvaz, On generalized derivations and Jordan ideals of prime rings, Rend. Circ. Mat. Palermo, II Ser., (2020), https://doi.org/10.1007/s12215-020-00492-8.