Graded weakly 1-absorbing prime ideals
- Ìnsal Tekir utekir@marmara.edu.tr
- Suat Koç suat.koc@medeniyet.edu.tr
- Rashid Abu-Dawwas rrashid@yu.edu.jo
- Eda Yıldız edyildiz@yildiz.edu.tr
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DOI:
https://doi.org/10.56754/0719-0646.2402.0291Abstract
In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let \(G\) be a group and \(R\) be a \(G\)-graded commutative ring with a nonzero identity \(1\neq0\). A proper graded ideal \(P\) of \(R\) is called a graded weakly 1-absorbing prime ideal if for each nonunits \(x,y,z\in h(R)\) with \(0\neq xyz\in P\), then either \(xy\in P\) or \(z\in P\). We give many properties and characterizations of graded weakly 1-absorbing prime ideals. Moreover, we investigate weakly 1-absorbing prime ideals under homomorphism, in factor ring, in rings of fractions, in idealization.
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