On Weakly 1-Absorbing Primary Ideals of Commutative Semirings

Authors : Mohammad SALEH, Ibaa MURAA

Pages : 199-208

Doi:10.33434/cams.1195074

View : 13 | Download : 9

Publication Date : 2022-12-30

Article Type : Research Paper

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