منابع مشابه
Associated Graphs of Modules Over Commutative Rings
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...
متن کاملNONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS
In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...
متن کاملEndomorphism Rings of Modules over Prime Rings
Endomorphism rings of modules appear as the center of a ring, as the fix ring of a ring with group action or as the subring of constants of a derivation. This note discusses the question whether certain ∗-prime modules have a prime endomorphism ring. Several conditions are presented that guarantee the primeness of the endomorphism ring. The contours of a possible example of a ∗-prime module who...
متن کاملModules over Differential Polynomial Rings
This note announces a number of results on the structure of differential modules over differential rings, where differential ring means a ring with a family of derivations and differential module means a module having a family of operators compatible with the derivations of the ring. To fix notation, throughout the paper we let A denote an associative ring, M = AM an 4-module, k the correspondi...
متن کاملJónsson Modules over Commutative Rings
Let M be an infinite unitary module over a commutative ring R with identity. Then M is called a Jónsson module provided every proper submodule of M has smaller cardinality than M. These modules have been studied by several algebraists, including Robert Gilmer, Bill Heinzer, and the author. In this note, we recall the major results on Jónsson modules to bring the reader up to speed on current re...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1960
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1960.10.607