On some Properties of Weakly Prime Semi-Ideals of Posets

Abstract

In this paper, we discuss some properties of direct product of weakly prime semi-ideals of P₁×P₂ where P₁ and P₂ are partially ordered sets (posets). We also find an equivalence condition for a semi-ideal to be weakly prime. Further we show that the semi-ideals are prime provided the direct product P of semi-ideals is a weakly prime semi-ideal of P, and the intersection of n distinct prime semi-ideals of P is a weakly (n+1)-prime semi-ideal of P.

Key words and phrases. Posets, direct product, semi-ideals, prime semi-ideals, weakly prime semi-ideals.

2000 Mathematics Subject Classification. 06D6