2-absorbing φ-δ-primary ideals

This paper aims to introduce 2-absorbing phi-delta-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 delta : I(A) -> I(A) is an expansion function and phi : I(A) -> I(A)U{theta} is a reduction function. A proper ideal Q of A is said to be a 2-absorbing phi-delta-primary if whenever abc is an element of Q - phi(Q), where a, b, c is an element of R, then either ab is an element of Q or ac is an element of delta(Q) or bc is an element of delta(Q). Various examples, properties, and characterizations of this new class of ideals are given.