Kyungpook Mathematical Journal

  • 제35권2호
  • /
  • Pages.223-223
  • /
  • 1995
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지

A Note on Multiplication Modules and Their Rings of Endomorphisms

Naoum, Adil G.;Al-Aubaidy, Wassan K.H.

  • 발행 : 19951200

⟨ 이전 논문 다음 논문 ⟩

초록

Let R be a commutative ring with 1, and let M be a (left) unitary R-module, let S = End(M) be the ring of R-endomorphisms of M. In this paper we look at some ring theoretic and module theoretic properties and try to see how do they transfer between R, S and M. Recall that an R-module M is said to be a multiplication R-module if each sub-module N of M has the form IM for some ideal I of R, [2]. In ${\S}1$ of this note we look at each of the Noetherian and Artinian properties and in ${\S}2$, we look at the regularity of R, and try to see how do they transfer to S.

키워드

참고문헌

  1. Introduction to commutative algebra Atiyah, M.F.;Macdonald, I.G.
  2. J. Algebra v.71 Multiplication modules Barnard, A.D.
  3. Comm. in Algebra v.16 Multiplication modules El-Bast, Z.A.;Smith, P.F.
  4. J. Math. Soc. Japan, v.13 On semihereditory rings Endo, S.
  5. Modules and rings Kasch, F.
  6. Commutative Algebra Knight, J.T.
  7. The theory of groups, Vol. 1 Kurosh, A.G.
  8. Lectures on rings and modules Lambek, J.
  9. Periodica Mathematica Hungarica v.21 On the ring of endomurphisms of finitely generated multiplication modules Naoum, A.G.
  10. Periodica IvIathematica Hungarica v.21 Flat modules and multiplication modules Naoum, A.G.
  11. Periodica Mathematica Hungarica v.29 On the ring of endomorphisms of multiplication modules Naoum, A.G.