On n-1-absorbing prime ideals.

In this paper, we introduce and study n -1-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 ∈ I for some nonunits x 1 , x 2 , ... , x n + 1 ∈ R , then either x 1 x 2 ... x n ∈ I or x n + 1 ∈ 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. [ABSTRACT FROM AUTHOR]