On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring

- Journal title : Kyungpook mathematical journal
- Volume 56, Issue 1, 2016, pp.107-120
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2016.56.1.107

Title & Authors

On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring

Soheilnia, Fatemeh;

Soheilnia, Fatemeh;

Abstract

Let R be a commutative semiring. The purpose of this note is to investigate the concept of 2-absorbing (resp., weakly 2-absorbing) primary ideals generalizing of 2-absorbing (resp., weakly 2-absorbing) ideals of semirings. A proper ideal I of R said to be a 2-absorbing (resp., weakly 2-absorbing) primary ideal if whenever such that (resp., ), then either or or . Moreover, when I is a Q-ideal and P is a k-ideal of R/I with , it is shown that if P is a 2-absorbing (resp., weakly 2-absorbing) primary ideal of R, then P/I is a 2-absorbing (resp., weakly 2-absorbing) primary ideal of R/I and it is also proved that if I and P/I are weakly 2-absorbing primary ideals, then P is a weakly 2-absorbing primary ideal of R.

Keywords

Semirings;Primary ideals;Weakly primary ideals;2-Absorbing primary ideals;Weakly 2-absorbing primary ideals;

Language

English

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