On (m,n)-closed ideals of commutative rings

Let Formula: see text be a commutative ring with Formula: see text, and let Formula: see text be a proper ideal of Formula: see text. Recall that Formula: see text is an Formula: see text-absorbing ideal if whenever Formula: see text for Formula: see text, then there are Formula: see text of the Formula: see text’s whose product is in Formula: see text. We define Formula: see text to be a semi-Formula: see text-absorbing ideal if Formula: see text for Formula: see text implies Formula: see text. More generally, for positive integers Formula: see text and Formula: see text, we define Formula: see text to be an Formula: see text-closed ideal if Formula: see text for Formula: see text implies Formula: see text. A number of examples and results on Formula: see text-closed ideals are discussed in this paper.