2008 / June Volume 3 No.2
Characterization of weakly prime subtractive ideals in semirings
| Published Date |
2008 / June
|
|---|---|
| Title | Characterization of weakly prime subtractive ideals in semirings |
| Author | |
| Keyword | |
| Download | |
| 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
|
| Received |
2007-08-23
|
| Accepted |
2007-08-23
|