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- W4287006344 abstract "This paper is concerned with S-co-m modules which are a generalization of co-m modules. In section 2, we introduce the S-small and S-essential submodules of a unitary $R$-module $M$ over a commutative ring $R$ with $1neq 0$ such that S is a multiplicatively closed subset of $R$. We prove that if $M$ is an S-co-m module satisfying the S-DAC and $Nleq M$, then $Nleq ^{S}_{e}M$ if and only if there exists $Ill ^{S}R$ such that $s(0:_{M}I)leq Nleq (0 :_{M}I)$ for some $sin S$. Let $M$ be a faithful S-strong co-m $R$-module. We prove that if $Nll ^{S}M$ then there exists an ideal $Ileq ^{S}_{e}R$ such that $s(0 :_{M}I)leq Nleq (0 :_{M}I)$. The converse is true if $S={1}$and $M$ is a prime module. In section 3, we introduce the S-quasi-copure submodules $N$ of an $R$-module $M$ and investigate some results related to this class of submodules." @default.
- W4287006344 created "2022-07-25" @default.
- W4287006344 creator A5007997807 @default.
- W4287006344 date "2021-09-01" @default.
- W4287006344 modified "2023-10-18" @default.
- W4287006344 title "S-small and S-essential submodules" @default.
- W4287006344 doi "https://doi.org/10.48550/arxiv.2109.00519" @default.
- W4287006344 hasPublicationYear "2021" @default.
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