baer's lower nilradical and classical prime submodules
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abstract
let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known. a formula to compute baer's lower nilradical of $n$ is given. the relations between classical prime submodules and their nilradicals are investigated. some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated.
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Baer's lower nilradical and classical prime submodules
Let $N$ be a submodule of a module $M$ and a minimal primary decomposition of $N$ is known. A formula to compute Baer's lower nilradical of $N$ is given. The relations between classical prime submodules and their nilradicals are investigated. Some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated.
full textbaer's lower nilradical and classical prime submodules
let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known. a formula to compute baer's lower nilradical of $n$ is given. the relations between classical prime submodules and their nilradicals are investigated. some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated.
full textOn graded classical prime and graded prime submodules
Let $G$ be a group with identity $e.$ Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce several results concerning graded classical prime submodules. For example, we give a characterization of graded classical prime submodules. Also, the relations between graded classical prime and graded prime submodules of $M$ are studied.
full textOn Graded Weakly Classical Prime Submodules
Let R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.
full texton graded classical prime and graded prime submodules
let $g$ be a group with identity $e.$ let $r$ be a $g$-graded commutative ring and $m$ a graded $r$-module. in this paper, we introduce several results concerning graded classical prime submodules. for example, we give a characterization of graded classical prime submodules. also, the relations between graded classical prime and graded prime submodules of $m$ are studied.
full textSome remarks on generalizations of classical prime submodules
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. Suppose that $phi:S(M)rightarrow S(M)cup lbraceemptysetrbrace$ be a function where $S(M)$ is the set of all submodules of $M$. A proper submodule $N$ of $M$ is called an $(n-1, n)$-$phi$-classical prime submodule, if whenever $r_{1},ldots,r_{n-1}in R$ and $min M$ with $r_{1}ldots r_{n-1}min Nsetminusphi(N)$, then $r_{1...
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Journal title:
bulletin of the iranian mathematical societyجلد ۴۰، شماره ۵، صفحات ۱۲۶۳-۱۲۷۴
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