Some Properties of Prime and Z-Semi-Ideals in Posets

[摘要] We define the notion of z-semi-ideals in a poset P and we show that if a z-semi-ideal J satisfies (∗)-property, then every minimal prime semiideal containing J is also a z-semi-ideal of P. We also show that every prime semi-ideal is a z-semi-ideal or the maximal z-semi-ideals contained in it are prime z-semi-ideals. Further, we characterize some properties of union of prime semi-ideals of P provided the prime semi-ideals are contained in the unique maximal semi-ideal of P.

[学科分类] 公共、环境与职业健康