Prufer conditions in an amalgamated duplication of a ring along an ideal

TL;DR

This paper explores how Prufer domain properties extend to rings with zero divisors via amalgamated duplication, providing new theoretical insights and examples in commutative algebra.

Contribution

It introduces novel ideal-theoretic and homological extensions of Prufer conditions to amalgamated duplications of rings along ideals.

Findings

Comparison with trivial ring extensions and pullbacks.

New families of rings satisfying Prufer conditions.

Original examples from amalgamated duplications.

Abstract

This paper investigates ideal-theoretic as well as homological extensions of the Prufer domain concept to commutative rings with zero divisors in an amalgamated duplication of a ring along an ideal. The new results both compare and contrast with recent results on trivial ring extensions (and pullbacks) as well as yield original families of examples issued from amalgamated duplications subject to various Prufer conditions.