Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: S-1-absorbing primary submodules   In this work, we introduce the notion of $S$-1-absorbing primary submodule as
an extension of 1-absorbing primary submodule. Let $S$ be a multiplicatively
closed subset of a ring $R$ and $M$ be an $R$-module. A submodule $N$ of $M$
with $(N:_{R}M)\cap S=\emptyset$ is said to be $S$-1-absorbing primary if
whenever $abm\in N$ for some non-unit $a,b\in R$ and $m\in M$, then either
$sab\in(N:_{R}M)$ or $sm\in M$-$rad(N)$. We examine several properties of this
concept and provide some characterizations. In addition, $S$-1-absorbing
primary avoidance theorem and $S $-1-absorbing primary property for
idealization and amalgamation are presented.

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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph