(2,n)-ideals of commutative rings

Let [Formula: see text] be commutative ring with [Formula: see text]. In this paper, we introduce a subclass of the class of [Formula: see text]-absorbing primary ideals called the class of [Formula: see text]-ideals. An ideal [Formula: see text] of [Formula: see text] with [Formula: see text] is called [Formula: see text]-ideal if whenever [Formula: see text] and [Formula: see text], then [Formula: see text] or [Formula: see text] or [Formula: see text]. Many examples and results are given to disclose the relations between this new concept and others that already exist. Namely, the prime ideals, the primary ideals, the 2-absorbing primary ideals, and the [Formula: see text]-ideals. Also, we use the [Formula: see text]-ideals to characterize some kind of rings.