On Weakly 1-Absorbing Primary Ideals of Commutative Semirings

Let R be a commutative semiring with 1 ≠0. In this paper, we study the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing ideal over commutative semirings . A proper ideal I of a semiring R is called a weakly 1-absorbing primary ideal if whenever nonunit elements a,b,c ∈ R and 0 ≠ abc ∈ I, then ab ∈ I, or c ∈ √I. A number of results concerning weakly 1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals are given. An ideal is called a subtractive ideal I of a semiring R is an ideal such that if x,x+y∈ I, then y∈ I. Subtractive ideals or k-ideals are helpful in proving in many results related to ideal theory over semirings.