On \phi-Prüfer and \phi-Bézout rings in amalgamation algebra along an ideal
Younes El Haddaoui
Department of Mathematics, Faculty of Sciences, University of Monastir, Tunisia.
Pages 178-186 | Received 08 September 2023, Accepted 13 December 2023, Published 30 June 2024
Abstract
In this paper, all rings considered are assumed commutative with nonzero identity. A ring R is said to be \phi-ring if its Nilradical is divided and prime ideal. The authors of [2] introduced and studied two new generalizations of Prüfer domains and Bézout domains respectively, a ring R is said to be \phi-Prüfer ring (resp., \phi-Bézout ring) provided that R/Nil(R) is a Prüfer domain (resp., a Bézout domain). In this work, we study the notions of \phi-Prüfer rings and \phi-Bézout ring in different contexts of commutative rings such us trivial ring extensions and amalgamations of algebras along ideals. Our aim is to generate new families of \phi-Prüfer rings and \phi-Bézout rings and also to enrich the literature with such a rings. Examples illustrating the aims and scopes of our results are given.
Keywords: \phi-Prüfer rings, \phi-Bézout rings, nonnil coherent rings, \phi-coherent rings.
MSC numbers: 13A15, 13A18, 13F05, 13G05, 13C20.
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