Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalizations of Graded $S$-Primary Ideals   The goal of this article is to present the graded weakly $S$-primary ideals
and $g$-weakly $S$-primary ideals which are extensions of graded weakly primary
ideals. Let $R$ be a commutative graded ring, $S\subseteq h(R)$ and $P$ be a
graded ideal of $R$. We state $P$ is a graded weakly $S$-primary ideal of $R$
if there exists $s\in S$ such that for all $x,y \in h(R)$, if $0\neq xy\in P$,
then $sx\in P$ or $sy\in Grad(P)$ (the graded radical of $P$). Several
properties and characteristics of graded weakly $S$-primary ideals as well as
graded $g$-weakly $S$-primary ideals are investigated.

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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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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: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci