On Weakly 1-Absorbing Primary Ideals of Commutative Rings

Abstract

Let R be a commutative ring with 1 not equal 0. We introduce the concept of weakly 1-absorbing primary ideal, which is a generalization of 1-absorbing primary ideal. A proper ideal I of R is said to be weakly 1-absorbing primary if whenever nonunit elements a, b,c is an element of R and 0 not equal abc is an element of I, we have ab is an element of I or c is an element of root I. A number of results concerning weakly 1-absorbing primary ideals are given, as well as examples of weakly 1-absorbing primary ideals. Furthermore, we give a corrected version of a result on 1-absorbing primary ideals of commutative rings.