Stone's topology for pseudocomplemented and bicomplemented lattices

Author:
P. V. Venkatanarasimhan

Journal:
Trans. Amer. Math. Soc. **170** (1972), 57-70

MSC:
Primary 06A35

DOI:
https://doi.org/10.1090/S0002-9947-1972-0311528-4

MathSciNet review:
0311528

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Abstract | References | Similar Articles | Additional Information

Abstract: In an earlier paper the author has proved the existence of prime ideals and prime dual ideals in a pseudocomplemented lattice (not necessarily distributive). The present paper is devoted to a study of Stone's topology on the set of prime dual ideals of a pseudocomplemented and a bicomplemented lattice.

If is the quotient lattice arising out of the congruence relation defined by in a pseudocomplemented lattice , it is proved that Stone's space of prime dual ideals of is homeomorphic to the subspace of maximal dual ideals of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0311528-4

Keywords:
Pseudocomplemented lattice,
bicomplemented lattice,
distributive lattice,
Boolean algebra,
normal element,
simple element,
prime ideal,
prime dual ideal,
quotient lattice,
Stone topology

Article copyright:
© Copyright 1972
American Mathematical Society