Pr\"ufer-Like Conditions in Subring Retracts and Applications
C. Bakkari, N. Mahdou, H. Mouanis
TL;DR
This paper explores five extensions of Pr"ufer domain concepts to rings with zero divisors, studying how these properties transfer between rings and their subring retracts, and providing new examples of such rings.
Contribution
It introduces five Pr"ufer-like conditions for rings with zero divisors and analyzes their transfer properties, expanding the class of known examples.
Findings
Transfer of Pr"ufer-like properties between rings and subring retracts
Construction of new examples of rings satisfying these conditions
Extension of Pr"ufer domain notions to rings with zero divisors
Abstract
In this paper, we consider five possible extensions of the Pr\"ufer domain notion to the case of commutative rings with zero divisors. We investigate the transfer of these Pr\"ufer-like properties between a commutative ring and its subring retract. Our results generate new families of examples of rings subject to a given Pr\"ufer-like conditions.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models