A generalization of graded prime hyperideals over graded multiplicative hyperrings

Abstract

Let [Formula: see text] be a group with identity [Formula: see text] and [Formula: see text] be a graded multiplicative hyperring. In this paper, we introduce and study the notion of graded [Formula: see text]-absorbing hyperideals of [Formula: see text] as a generalization of prime hyperideals. Many properties, examples and characterizations of graded [Formula: see text]-absorbing hyperideals of [Formula: see text] are introduced. Moreover, we investigate the behavior of this structure under homogeneous components, graded hyperring homomorphisms, Cartesian product and fundamental relations. We consider the fundamental relation [Formula: see text] on [Formula: see text] as the smallest equivalence relation such that the quotient [Formula: see text] is a ring. Also, we show that if [Formula: see text] is a graded hyperring, then [Formula: see text] is a graded ring.