Prûfer property in amalgamated algebras along an ideal

Abstract

Let $f:A\to B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we give a characterization of zero divisors of the amalgamation which is a generalization of Maimani's and Yassemi's work (see \cite{y}). Also, we investigate the transfer of Prüfer domain concept to commutative rings with zero divisors in the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A{\bowtie }^{f}J),$ introduced and studied by D'Anna, Finocchiaro and Fontana in 2009 (see \cite{AFF1} and \cite{AFF2}). Our aim is to provide new classes of commutative rings satisfying this property.

arXiv admin note: text overlap with arXiv:1001.0472 by other authors

References in corpus (1)

• The amalgamated duplication of a ring along a multiplicative-canonical ideal