Amalgamated algebras along an ideal defined by 1-absorbing-like conditions

Abstract

Let R be a commutative ring with nonzero identity. A proper ideal I of R is called a 1-absorbing prime ideal (respectively, 1-absorbing primary ideal) if whenever nonunit elements a,b,c is an element of R with abc is an element of I, then ab is an element of I or c is an element of I (respectively, ab is an element of I or c is an element of root I). The purpose of this paper is to study the transfer of certain 1-absorbing-like properties to amalgamation of A with B along J with respect to f (denoted by A?(f)J), introduced and studied by D'Anna, Finocchiaro and Fontana. Our results provide new techniques for the construction of new original examples satisfying the above-mentioned properties.