Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Weakly 1-Absorbing Prime Ideals   This paper introduce and study weakly 1-absorbing prime ideals in commutative
rings. Let $A$ be a commutative ring with a nonzero identity $1\neq 0$. A
proper ideal $P$ of $A$ is said to be a weakly 1-absorbing prime ideal if for
each nonunits $x, y, z \in A$ with $0\neq xyz \in P$, then either $xy \in P$ or
$z \in P$. In addition to give many properties and characterizations of weakly
1-absorbing prime ideals, we also determine rings in which every proper ideal
is weakly 1-absorbing prime. Furthermore, we investigate weakly 1-absorbing
prime ideals in $C(X)$, which is the ring of continuous functions of a
topological space X.

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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an