baer's lower nilradical and classical prime submodules
نویسندگان
چکیده
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.
منابع مشابه
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.
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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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عنوان ژورنال:
bulletin of the iranian mathematical societyجلد ۴۰، شماره ۵، صفحات ۱۲۶۳-۱۲۷۴
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