2008 / June Volume 3 No.2
Characterization of weakly prime subtractive ideals in semirings
Published Date |
2008 / June
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Title | Characterization of weakly prime subtractive ideals in semirings |
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Pagination | 347-352 |
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 $I \sqrt{0} = 0$. |
AMS Subject Classification |
16Y60
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Received |
2007-08-23
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Accepted |
2007-08-23
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