Journal Article10.1080/00927879708825941
Cyclically decomposable distributive modules
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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.
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Abstract: Let R be a ring and M an R-module. Then M is said to be distributive if the lattice of submodules of M is distributive. We 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.
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Citations
The Homomorphisms of Distributive Semimodules
Ali Hasan Abdulkhaliq,Asaad M. A. Alhossaini +1 more
TL;DR: The homomorphisms of distributive semimodules are studied. Some results are generalized and new conditions are introduced to get good results. Relationships between distributive semimodules and other concepts are obtained.
2
Modules with distributive submodule lattice
Askar A. Tuganbaev
- 01 Jan 2000
TL;DR: In this paper, the distributivity of a commutative ring A is equivalent to the fact that all localizations of A, its maximal ideals are uniserial rings; the commutativity case deserves a special consideration.
1
On graded distributive modules
TL;DR: In this paper, the characterizations of graded distributive modules are investigated and several characterisations of the identity of a distributive module are given. But these characterizations are restricted to Ω-grained commutative rings with identity.
Characterizations of graded distributive modules
Zamani Naser
- 01 Jan 2008
TL;DR: In this paper, several characterizations of graded distributive modules are investigated, and a Z-grained commutative ring with identity is defined, where R is defined as a distributive distributive module with identity.
References
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Multiplication modules which are distributive
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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Joseph J. Rotman
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TL;DR: An Introduction to Homological Algebra as discussed by the authors discusses the origins of algebraic topology and presents the study of homological algebra as a two-stage affair: first, one must learn the language of Ext and Tor and what it describes.