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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Stone’s topology for pseudocomplemented and bicomplemented lattices
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by P. V. Venkatanarasimhan PDF
Trans. Amer. Math. Soc. 170 (1972), 57-70 Request permission

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
  • © Copyright 1972 American Mathematical Society
  • 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