Some Results on Pure Submodules Relative to Submodule
نویسندگان
چکیده
منابع مشابه
SOME RESULTS ON STRONGLY PRIME SUBMODULES
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)ysubseteq P$ for $x, yin M$, implies that $xin P$ or $yin P$. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated $R$-module $M$ is Artinian if and only if $M$ is Noetherian and every st...
متن کاملS-pure Submodules
Purity in module categories and its different generalizations have been present in the literature since the 1960s. Apart from its special role in module theory, the importance of purity increased during the last two decades through the developments of model theory and the study of locally finitely presented categories (e.g., [2, 6]). In the module theory context, that will be our framework, a p...
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Let $R$ be an arbitrary ring and $T$ be a submodule of an $R$-module $M$. A submodule $N$ of $M$ is called $T$-small in $M$ provided for each submodule $X$ of $M$, $Tsubseteq X+N$ implies that $Tsubseteq X$. We study this mentioned notion which is a generalization of the small submodules and we obtain some related results.
متن کاملsome results on strongly prime submodules
let $r$ be a commutative ring with identity and let $m$ be an $r$-module. a proper submodule $p$ of $m$ is called strongly prime submodule if $(p + rx : m)ysubseteq p$ for $x, yin m$, implies that $xin p$ or $yin p$. in this paper, we study more properties of strongly prime submodules. it is shown that a finitely generated $r$-module $m$ is artinian if and only if $m$ is noetherian and every st...
متن کاملPure Submodules of Multiplication Modules
The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...
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ژورنال
عنوان ژورنال: Baghdad Science Journal
سال: 2015
ISSN: 2411-7986,2078-8665
DOI: 10.21123/bsj.12.4.833-837