On n-1-absorbing prime ideals

Abstract

In this paper, we introduce and study n-i-absorbing prime ideals of commutative rings. Let R be a ring and n a positive integer. A proper ideal I of R is said to be an n-1-absorbing prime ideal if whenever x(1)x(2) ... x(n+1) is an element of I for some nonunits x(1), x(2), ..., x(n+1) is an element of R, then either x(1)x(2) ... x(n) is an element of I or x(n+1) is an element of I. It is obvious that 1-1-absorbing (2-1-absorbing) prime ideals are exactly prime (1-absorbing prime) ideals. Various examples and characterizations of n-1-absorbing prime ideals are given.