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;

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 $\small{a,b,c{\in}R}$ such that $\small{abc{\in}I}$ (resp., $\small{0{\neq}abc{\in}I}$), then either $\small{ab{\in}I}$ or $\small{bc{\in}\sqrt{I}}$ or $\small{ac{\in}\sqrt{I}}$. Moreover, when I is a Q-ideal and P is a k-ideal of R/I with $\small{I{\subseteq}P}$, 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
Cited by
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