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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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: 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 $ \hat L$ is the quotient lattice arising out of the congruence relation defined by $ a \equiv b \Leftrightarrow {a^ \ast } = {b^ \ast }$ in a pseudocomplemented lattice $ L$, it is proved that Stone's space of prime dual ideals of $ \hat L$ is homeomorphic to the subspace of maximal dual ideals of $ L$.


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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