sigma$-Prime Spectrum of Almost Distributive Lattices

For each $\alpha$-ideal of an almost distributive lattice (ADL) to become a $\sigma$-ideal, a set of equivalent conditions is derived, which tends to result in a characterization of generalized Stone ADLs.  On an ADL, a one-to-one correspondence is derived between the set of all prime $\sigma$-ideal...

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Published inEuropean journal of pure and applied mathematics Vol. 17; no. 2; pp. 1094 - 1112
Main Authors Noorbhasha, Rafi, Bandaru, Ravikumar, Iampan, Aiyared
Format Journal Article
LanguageEnglish
Published 01.04.2024
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Summary:For each $\alpha$-ideal of an almost distributive lattice (ADL) to become a $\sigma$-ideal, a set of equivalent conditions is derived, which tends to result in a characterization of generalized Stone ADLs.  On an ADL, a one-to-one correspondence is derived between the set of all prime $\sigma$-ideals of the ADL and the set of all prime $\sigma$-ideals of the quotient ADL. Finally, proved some properties of prime $\sigma$-ideals of a normal ADL topologically.
ISSN:1307-5543
1307-5543
DOI:10.29020/nybg.ejpam.v17i2.5098