S-2-Absorbing ideals and their relationship with right S-prime ideals in noncommutative rings

This paper introduces and investigates the concept of [Formula: see text]-[Formula: see text]-absorbing ideals in the context of noncommutative rings. Building on the notions of [Formula: see text]-absorbing ideals and [Formula: see text]-prime ideals, an ideal [Formula: see text] of a ring [Formula: see text], disjoint from an [Formula: see text]-system [Formula: see text], is defined as an [Formula: see text]-[Formula: see text]-absorbing ideal if, for all [Formula: see text] with [Formula: see text], there exists [Formula: see text] such that [Formula: see text], [Formula: see text], or [Formula: see text]. We examine fundamental properties of [Formula: see text]-[Formula: see text]-absorbing ideals, demonstrating their distinctions from related concepts such as [Formula: see text]-absorbing and [Formula: see text]-prime ideals. Further, we explore [Formula: see text]-[Formula: see text]-absorbing ideals in various ring constructions. We show in rings in which every [Formula: see text]-[Formula: see text]-absorbing ideal is right [Formula: see text]-prime ([Formula: see text]-[Formula: see text]-AB rings), the set of right [Formula: see text]-prime ideals is [Formula: see text]-totally ordered, and the prime radical [Formula: see text] forms a right [Formula: see text]-prime ideal.