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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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The structure of pseudocomplemented distributive lattices. II. Congruence extension and amalgamation
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by G. Grätzer and H. Lakser PDF
Trans. Amer. Math. Soc. 156 (1971), 343-358 Request permission

Abstract:

This paper continues the examination of the structure of pseudocomplemented distributive lattices. First, the Congruence Extension Property is proved. This is then applied to examine properties of the equational classes ${\mathcal {B}_n}, - 1 \leqq n \leqq \omega$, which is a complete list of all the equational classes of pseudocomplemented distributive lattices (see Part I). The standard semigroups (i.e., the semigroup generated by the operators H, S, and P) are described. The Amalgamation Property is shown to hold iff $n \leqq 2$ or $n = \omega$. For $3 \leqq n < \omega ,{\mathcal {B}_n}$ does not satisfy the Amalgamation Property; the deviation is measured by a class Amal $({\mathcal {B}_n})( \subseteq {\mathcal {B}_n})$. The finite algebras in Amal $({\mathcal {B}_n})$ are determined.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 156 (1971), 343-358
  • MSC: Primary 06.50
  • DOI: https://doi.org/10.1090/S0002-9947-1971-0274359-9
  • MathSciNet review: 0274359