Rings in which every S-prime ideal is prime
Chahrazade Bakkari\,^1 and Rachid Hachachei\,^2
\,^{1,2}Department of Mathematics, Faculty of Science, University Moulay Ismail Meknes, Morocco
Pages 38-45 | Received 09 May 2024, Accepted 15 November 2024, Published 10 July 2025
Abstract
In this paper, we study the S–\alpha-ring property, that is a ring in which every S-prime ideal is prime. We investigate the possible transfer of this property to various context of commutative ring extensions including homomorphic image, localization, trivial ring extensions and amalgamation rings. Our results provide new classes of commutative rings satisfying the above property.
Keywords: S-prime ideal, prime ideal, S–\alpha-ring, localization, trivial ring extension, amalgamation ring.
MSC numbers: 13F05, 13A15, 13E05, 13F20, 13C10, 13C11, 13F30, 13D05.
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