On Pr\"ufer-like conditions
Chahrazade Bakkari
TL;DR
This paper explores five extensions of Pr"ufer domains to rings with zero divisors, analyzing their stability under localization and homomorphic images, and providing new examples of such rings.
Contribution
It introduces five new Pr"ufer-like conditions for rings with zero divisors and studies their stability, offering original examples and insights.
Findings
Identified stability properties of Pr"ufer-like conditions under localization and homomorphic images.
Generated new examples of rings satisfying these Pr"ufer-like conditions.
Extended the concept of Pr"ufer domains to rings with zero divisors.
Abstract
This paper deals with five extensions of the Pr\"ufer domain concept to commutative rings with zero divisors. We investigate the stability of these Pr\"ufer-like conditions under localization and homomorphic image. Our results generate new and original examples of Pr\"ufer-like rings.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models