On Weakly 1-Absorbing Primary Ideals of Commutative Semirings

Year 2022, Volume: 5 Issue: 4, 199 - 208, 30.12.2022

Mohammad Saleh , Ibaa Muraa

https://doi.org/10.33434/cams.1195074

Cited By: 2

Abstract

Let $R$ be a commutative semiring with $ 1 \neq0$. In this paper, we study the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing ideal over commutative semirings . A proper ideal $I$ of a semiring $R$ is called a weakly 1-absorbing primary ideal if whenever nonunit elements $a,b,c \in R$ and $0 \neq abc \in I$, then $ab \in I $, or $c \in \sqrt{I}$. A number of results concerning weakly 1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals are given. An ideal is called a subtractive ideal $I$ of a semiring $R$ is an ideal such that if $ x,x+y\in I$, then $ y\in I$. Subtractive ideals or k-ideals are helpful in proving in many results related to ideal theory over semirings.

Keywords

prime ideal , weakly primary , 1-absorbing primary ideal , 2-absorbing primary ideal , weakly 1-absorbing primary ideal , weakly 2-absorbing primary ideal , weakly primary ideal , weakly prime ideal

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