On k-Weakly Primary Ideals Over Semirings

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 A² = 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