On Weakly 1-Absorbing Primary Ideals of Commutative Semirings

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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Communications in Advanced Mathematical Sciences-Cover

ISSN: 2651-4001
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2018
Yayıncı: Emrah Evren KARA

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