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- W2997088545 abstract "Let $R$ be a commutative ring with identity and $M$ be an $R$-module. In this paper, in order to study prime submodules, radical submodules and primary decompositions in finitely generated free $R$-modules, we introduce and study an operation $Delta: (Moplus R)^2to M$ defined by $Delta(m+r, m'+r')= r'm-rm'$. In particular, using this operation we give a characterization of prime submodules of $Moplus R$, in terms of prime submodules of $M$. As an application, we present a characterization of prime submodules of finitely generated free modules. Also we present a formula for the prime radical of submodules of $Mdis R$. Moreover, we state some conditions under which primary decompositions of submodules of $M$ lift to $Moplus R$." @default.
- W2997088545 created "2020-01-10" @default.
- W2997088545 creator A5036637052 @default.
- W2997088545 date "2020-08-06" @default.
- W2997088545 modified "2023-09-27" @default.
- W2997088545 title "Delta operation on modules, prime and radical submodules and primary decomposition" @default.
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- W2997088545 doi "https://doi.org/10.15672/hujms.667410" @default.
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