On n-1-absorbing prime ideals

Abstract

In this paper, we introduce and study [Formula: see text]-1-absorbing prime ideals of commutative rings. Let [Formula: see text] be a ring and [Formula: see text] a positive integer. A proper ideal [Formula: see text] of [Formula: see text] is said to be an [Formula: see text]-1-absorbing prime ideal if whenever [Formula: see text] for some nonunits [Formula: see text] then either [Formula: see text] or [Formula: see text] It is obvious that 1-1-absorbing (2-1-absorbing) prime ideals are exactly prime (1-absorbing prime) ideals. Various examples and characterizations of [Formula: see text]-1-absorbing prime ideals are given.