On 2-absorbing primary ideals in commutative semirings

Abstract

In this paper, we define 2-absorbing and weakly 2-absorbing primary ideals in a commutative semiring S with 1 ≠ 0 which are generalization of primary ideals of commutative ring. A proper ideal I of a commutative semiring S is said to be a 2-absorbing primary (weakly 2-absorbing primary) ideal of S if abc ∈ I (0 ≠ abc ∈ I) implies ab ∈ I or bc ∈ √ I or ac ∈ √ I. Some results concerning 2- absorbing primary and weakly 2-absorbing primary ideals are given. It is proved that a subtractive weakly 2-absorbing primary ideal I that is not a 2-absorbing primary ideal satisfies √ I = √ 0.