Characterization of weakly prime subtractive ideals in semirings
by Vishnu Gupta   J. N. Chaudhari  

Vol. 3 No. 2 (2008) P.347~P.352

ABSTRACT

In the paper we extend some results of [1] to non commutative semirings with $1 \neq 0$. We prove the following Theorem:
(1) Let $I$ be a subtractive ideal of a semiring $R$. Then $I$ is a weakly prime ideal of $R$ if and only if for left ideals $A$ and $B$ of $R$, $0 \neq AB \subseteq I$ implies that $A \subseteq I$ or $B \subseteq I$.
(2) Let $R$ be a semiring in which all nilpotent elements are central and let $I$ be a weakly prime subtractive ideal of $R$ which is not a prime ideal of $R$. Then $I \sqrt{0} = 0$.

KEYWORDS
Semiring, subtractive ideal, prime ideal, weakly prime ideal

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 16Y60

MILESTONES

Received: 2007-05-22
Revised : 2007-08-23
Accepted: 2007-08-23

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