Normal Paradistributive Latticoids

Abstract

For any filter $\LomP$ of a paradistributive latticoid, $\LomO(\LomP)$ is defined and it is proved that $\LomO(\LomP)$ is a filter if $\LomP$ is prime. It is also proved that each minimal prime filter belonging to $\LomO(\LomP)$ is contained in $\LomP$, and $\LomO(\LomP)$ is the intersection of all the minimal prime filters contained in $\LomP$. The concept of a normal paradistributive latticoid is introduced and characterized in terms of the prime filters and minimal prime filters. We proved that every relatively complemented paradistributive latticoid is normal.