On ϕ-S-1-absorbing δ-primary superideals over commutative super-rings

Abstract

Let [Formula: see text] be a commutative super-ring with unity [Formula: see text] and let [Formula: see text] be the set of all superideals of [Formula: see text]. Let [Formula: see text] be a reduction function of superideals of [Formula: see text] and let [Formula: see text] be an expansion function of superideals of [Formula: see text]. We recall that a proper superideal [Formula: see text] of [Formula: see text] is called a [Formula: see text]-1-absorbing [Formula: see text]-primary superideal of [Formula: see text], if whenever [Formula: see text] for some nonunit elements [Formula: see text], then [Formula: see text] or [Formula: see text]. In this paper, we introduce a new class of superideals that is a generalization to the class of [Formula: see text]-1-absorbing [Formula: see text]-primary superideals. Let [Formula: see text] be a multiplicative subset of the subset [Formula: see text] of the homogeneous elements such that [Formula: see text] and let [Formula: see text] be a proper superideal of [Formula: see text] with [Formula: see text], then [Formula: see text] is called a [Formula: see text]-[Formula: see text]-1-absorbing [Formula: see text]-primary superideal of [Formula: see text] associated to [Formula: see text] if whenever [Formula: see text] for some nonunit elements [Formula: see text], then [Formula: see text] or [Formula: see text]. In this paper, we have presented a range of different examples, properties and characterizations of this new class of superideals.