Abstract:In this paper, we study the concepts of 2-absorbing and weakly 2-absorbing ideals in a commutative semiring with non-zero identity which is a generalization of prime ideals of a commutative semiring and prove number of results related to the same. We also use these concepts to prove some results of Q-ideals in terms of subtractive extension of ideals in a commutative semiring.
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 ofWe also introduce the concept of 2-absoring 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.
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