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On Weakly 1-Absorbing Prime Ideals

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Suat Koç, Ünsal Tekir, Eda Y{i}ld{i}z

Commutative Algebra · Submitted 20 May 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID2005.10365 (version 1)
Pith IDHSSJZ5CO, Pith's permanent record of this paper and its review
CitationEda Y{\i}ld{\i}z, Suat Ko\c{c}, \"Unsal Tekir. "On Weakly 1-Absorbing Prime Ideals." arXiv:2005.10365 (2020). https://pith.science/paper/HSSJZ5CO
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arXiv listing abstract v1. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. contribution 1.00 0.91 0.11 asserted 0.98
s1 Let $A$ be a commutative ring with a nonzero identity $1\neq 0$. background 1.00 0.08 0.02 asserted 0.88
s2 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 $z \in P$. contribution 0.74 0.38 0.07 asserted 0.99
s3 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. contribution 0.94 0.96 0.25 asserted 1.00
s4 Furthermore, we investigate weakly 1-absorbing prime ideals in $C(X)$, which is the ring of continuous functions of a topological space X. contribution 1.00 0.93 0.07 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Original abstract

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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