TY - JOUR
TI - Normal Paradistributive Latticoids
PY - 2024/04/30
Y2 - 2024/08/05
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 17
IS - 2
DO - 10.29020/nybg.ejpam.v17i2.5127
UR - https://doi.org/10.29020/nybg.ejpam.v17i2.5127
SP - 1306-1320
AB - 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.
ER -