On $k$-Weakly Primary Ideals Over Semirings
DOI:
https://doi.org/10.5644/SJM.03.1.02Keywords:
Semirings, $k$-ideals, weakly prime, weakly primaryAbstract
Since ideals in rings and semirings are closely related, two-sided $k$-ideals occur frequently in semiring theory. Let $R$ be a commutative semiring. For an ideal of $R$, the notion of $k$-weakly primary ideals is defined. It is shown that this notion inherits most of the essential properties of the weakly primary ideals of a commutative ring (see [1], [4]). For example, it is proved that a $k$-weakly primary ideal $A$ of $R$, that is not primary, satisfies $A^{2} = 0$ and rad ($A$) = rad (0). Also, it is shown that an intersection of a family of $k$-weakly primary ideals, that are not primary, is $k$-weakly primary.
2000 Mathematics Subject Classification. 16Y60
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