QUASI-PRIMARY IDEALS IN COMMUTATIVE SEMIRINGS.

In this paper, we define quasi-primary ideals in commutative semirings S with 1 ≠ 0 which is a generalization of primary ideals. A proper ideal I of a semiring S is said to be a quasi-primary ideal of S if ab ∈ √I implies a ∈ √I or b ∈ √I. We also introduce the concept of 2-absorbing quasi-primary ideal of a semiring S which is a generalization of quasi-primary ideal of S. A proper ideal I of a semiring S is said to be a 2-absorbing quasi-primary ideal if abc ∈ √I implies ab ∈ √I or bc ∈ √I or ac ∈ √I. Some basic results related to 2-absorbing quasi-primary ideal have also been given. [ABSTRACT FROM AUTHOR]