On 2-absorbing primary ideals in commutative semirings
Keywords:Semiring, subtractive ideal, 2-absorbing} primary ideal, weakly 2-absorbing primary ideal, Q-ideal.
AbstractIn this paper, we define 2-absorbing and weakly 2-absorbing primary ideals in a commutative semiring S with 1 â‰ 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 âˆˆ I (0 â‰ abc âˆˆ I) implies ab âˆˆ I or bc âˆˆ âˆš I or ac âˆˆ âˆš 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 âˆš I = âˆš 0.
How to Cite
Sarohe, P., & Dubey, manish kant. (2016). On 2-absorbing primary ideals in commutative semirings. European Journal of Pure and Applied Mathematics, 9(2), 186–195. Retrieved from https://ejpam.com/index.php/ejpam/article/view/2272
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