Graded weakly 1-absorbing prime ideals

  • Ünsal Tekir Department of Mathematics, Marmara University, Istanbul, Turkey.
  • Suat Koç Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey.
  • Rashid Abu-Dawwas Department of Mathematics, Yarmouk University, Jordan.
  • Eda Yıldız Department of Mathematics, Yildiz Technical University, Istanbul, Turkey.
Keywords: graded ideal, 1-absorbing prime ideal, weakly 1-absorbing prime ideal, graded weakly 1-absorbing prime ideal

Abstract

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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Published
2022-08-22
How to Cite
[1]
Ünsal Tekir, S. Koç, R. Abu-Dawwas, and E. Yıldız, “Graded weakly 1-absorbing prime ideals”, CUBO, vol. 24, no. 2, pp. 291–305, Aug. 2022.
Section
Articles