Graded Amalgamated Algebras Along an Ideal Defined by Graded 1-Absorbing-Like Conditions

Let Formula: see text be a group with identity and Formula: see text be a Formula: see text-graded commutative ring with nonzero identity. A proper graded ideal Formula: see text of Formula: see text is called a graded 1-absorbing prime ideal (respectively, graded 1-absorbing primary ideal) if whenever nonunit homogeneous elements Formula: see text with Formula: see text, then Formula: see text or Formula: see text (respectively, Formula: see text or Formula: see text, where Formula: see text is the graded radical of Formula: see text). The purpose of this paper is to study the transfer of some graded 1-absorbing-like properties to the graded amalgamated algebra along an ideal (denoted by Formula: see text). Our results provide new techniques for the construction of new original examples satisfying the above-mentioned properties.