2-absorbing φ-δ -primary ideals

Abstract

This paper aims to introduce 2-absorbing φ-δ -primary ideals over commutative rings which unify the concepts of all generalizations of 2-absorbing and 2-absorbing primary ideals. Let A be a commutative ring with a nonzero identity and I(A) be the set of all ideals of A. Suppose that δ : I(A) → I(A) is an expansion function and φ : I(A) → I(A)∪{∅} is a reduction function. A proper ideal Q of A is said to be a 2-absorbing φ-δ -primary if whenever abc ∈ Q − φ(Q), where a, b, c ∈ R, then either ab ∈ Q or ac ∈ δ(Q) or bc ∈ δ(Q). Various examples, properties, and characterizations of this new class of ideals are given.