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On 2-Absorbing Primary Ideals in Commutative Semirings

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2016

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Abstract (2. Language): 
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.
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REFERENCES

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