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On weakly 1-absorbing prime ideals

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Abstract

This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let \(A\ \)be a commutative ring with a nonzero identity \(1\ne 0.\) A proper ideal \(P\ \)of \(A\ \)is said to be a weakly 1-absorbing prime ideal if for every nonunits \(x,y,z\in A\ \)with \(0\ne xyz\in P,\ \)then \(xy\in P\) 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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Acknowledgements

The authors would like to thank the referee for his/her great efforts in proofreading the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Marmara University, Istanbul, Turkey

    Suat Koç & Ünsal Tekir

  2. Department of Mathematics, Yildiz Technical University, Istanbul, Turkey

    Eda Yıldız

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  1. Suat Koç
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  2. Ünsal Tekir
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  3. Eda Yıldız
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Correspondence to Ünsal Tekir.

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Koç, S., Tekir, Ü. & Yıldız, E. On weakly 1-absorbing prime ideals. Ricerche mat 72, 723–738 (2023). https://doi.org/10.1007/s11587-020-00550-4

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  • DOI: https://doi.org/10.1007/s11587-020-00550-4

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