Normal Paradistributive Latticoids

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...

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Published inEuropean journal of pure and applied mathematics Vol. 17; no. 2; pp. 1306 - 1320
Main Authors Bandaru, Ravikumar, Patel, Prashant, Rafi, Noorbhasha, Shukla, Rahul, Ajjarapu, Suryavardhani
Format Journal Article
LanguageEnglish
Published 01.04.2024
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Summary: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.
ISSN:1307-5543
1307-5543
DOI:10.29020/nybg.ejpam.v17i2.5127