Multiplication modules which are distributive
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TL;DR: In this paper, necessary and sufficient conditions for a multiplication module to be distributive were proved and proved. But they did not consider the case of a single multiplication module with two multiplication modules.
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About: This article is published in Journal of Pure and Applied Algebra. The article was published on 01 Oct 1988. and is currently open access. The article focuses on the topics: Multiplication & Distributive property.
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Citations
•Journal Article
Multiplication Modules and characteristic submodules
Young Soo Park,Chang Woo Choi +1 more
TL;DR: In this paper, it was shown that a ring R is a multiplication module if for every submodule N of R there exists an ideal I of R such that N = IM.
7
Finitely generated graded multiplication modules
TL;DR: In this article, it was shown that any graded submodule of a finitely generated generalised graded multiplication R-module M has a kind of primary decomposition, and a characterisation of graded primary submodules of M was given.
Cyclically decomposable distributive modules
TL;DR: In this paper, the authors determine the structure of distributive modules, and show that in certain cases a distributive module is either cyclic or is a direct sum of cyclic submodules.
5
Cohen-Macaulayness of multiplication rings and modules
TL;DR: In this paper, it was shown that a non-zero nitely generated multiplication R-module is a Cohen-Macaulay module whenever R is Noetherian, and when this is the case and R is commutative, the N-height of a (written htN a) is the supremum of the lengths of chains of prime ideals of Supp(N) terminating with p.