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

Let [Formula: see text] be a commutative ring with nonzero identity. A proper ideal [Formula: see text] of [Formula: see text] is called a 1-absorbing prime ideal (respectively, 1-absorbing primary ideal) if whenever nonunit elements [Formula: see text] with [Formula: see text] then [Formula: see text] or [Formula: see text] (respectively, [Formula: see text] or [Formula: see text]). The purpose of this paper is to study the transfer of certain 1-absorbing-like properties to amalgamation of [Formula: see text] with [Formula: see text] along [Formula: see text] with respect to [Formula: see text] (denoted by [Formula: see text]), 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.