Graded φ-2-absorbing hyperideals in graded multiplicative hyperrings

Abstract

Let [Formula: see text] be an abelian group with identity [Formula: see text]. Let [Formula: see text] be a graded multiplicative hyperring and [Formula: see text] be a function where [Formula: see text] is the set of graded hyperideals of [Formula: see text] and [Formula: see text] for every graded hyperideal [Formula: see text] of [Formula: see text]. In this paper, we introduce and study the concepts of graded [Formula: see text]-[Formula: see text]-absorbing hyperideals and graded [Formula: see text]-[Formula: see text]-absorbing primary hyperideals of [Formula: see text]. Moreover, we give a number of main results and the basic properties concerning these classes of graded hyperideals and their homogeneous components.