Rings in which every nonzero S-weakly prime ideal is weakly prime
Chahrazade Bakkari\,^1 and Hamza El-Mzaiti\,^2
\,^{1,2}Department of Mathematics, Faculty of Science, University Moulay Ismail, Meknes, Morocco
Pages 338-344 | Received 02 February 2024, Accepted 30 May 2024, Published 08 November 2024
Abstract
In this paper, we introduce and study a new class of rings with multiplicative subset S which we’ll call S-ME-rings. A ring R with a multiplicative subset S is said to be S-ME-ring if every non-zero S-weakly prime ideal of R is weakly prime. We next study the possible transfer of the properties of being S-ME-ring in the homomorphic image, in the trivial ring extensions and the amalgamated algebra along an ideal introduced and studied by the authors of [6, 7, 8, 9]. Our results allow us to construct new original class of S-ME-rings subject to various ring theoretical properties.
MSC numbers: Primary 11R20, 11R29; Secondary 13F20.
Downloads: Full-text PDF