Rings in which every ideal disjoint with \(S\) is \(S\)-almost prime

Chahrazade Bakkari; Rachid Hachache; Najib Mahdou; Unsal Tekir; Ece Yetkin Celikel

doi:10.56754/0719-0646.2802.349

DOI:

https://doi.org/10.56754/0719-0646.2802.349

Abstract

Let \(R\) be a commutative ring with identity and \(S\) a multiplicative subset of \(R\). In this study, we introduce the concept of rings in which every ideal disjoint with \(S\) is \(S\)-almost prime. We investigate the possible transfer of the above ring property in the quotient rings, localizations, direct products, trivial ring extensions, and amalgamation algebra.

Keywords

S-almost prime ideal , S-prime ideal , AP-rings

Mathematics Subject Classification:

13A15 , 13A99

Chahrazade Bakkari Department of Mathematics, Faculty of Science, University Moulay Ismail Meknes, Morocco. https://orcid.org/0000-0002-6387-7972
Rachid Hachache Department of Mathematics, Faculty of Science, University Moulay Ismail Meknes, Morocco.
Najib Mahdou Laboratory of Modelling and Mathematical Structures, Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S.M. Ben Abdellah Fez, Morocco. https://orcid.org/0000-0001-6353-1114
Unsal Tekir Department of Mathematics, Marmara University, Istanbul, Türkiye. https://orcid.org/0000-0003-0739-1449
Ece Yetkin Celikel Department of Software Engineering, Faculty of Engineering, Hasan Kalyoncu University, Gaziantep, Türkiye. https://orcid.org/0000-0001-6194-656X

Pages: 349-362
Date Published: 2026-05-27
Vol. 28 No. 2 (2026)

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