Abstract
Recently, Grätzer, Gunderson and Quackenbush have characterized the spectra of finite pseudocomplemented lattices, solving a problem raised by G. Grätzer in his first monograph on lattice theory from 1971. In this note we discuss the tight connection between the spectra and the Glivenko congruence of finite pseudocomplemented lattices.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Birkhoff G.: Lattice Theory, 3rd edn. American Mathematical Society, Providence (1967)
Frink O.: Pseudo-complements in semi-lattices. Duke Math. J. 29, 505–514 (1962)
Glivenko V.: Sur quelques points de la logique de M. Brouwer. Bull Acad. Sci. Belgique 15, 183–188 (1929)
Grätzer G.: Lattice Theory First. Concepts and Distributive Lattices. W. H. Freeman and Co., San Francisco (1971)
Grätzer G.: General Lattice Theory, 2nd edn. Birkhäuser, Basel (1998)
Grätzer G., Gunderson D.S., Quackenbush R.W.: The spectrum of a finite pseudocomplemented lattice. Algebra Universalis 61, 407–411 (2009)
Jacobson N.: Lectures in Abstract Algebra, vol. I. D. van Nostrand, Princeton (1964)
Katriňák T.: Subdirectly irreducible modular p-algebras. Algebra Universalis 2, 166–173 (1972)
Katriňák T.: A new proof of the construction theorem for Stone algebras. Proc. Amer. Math. Soc. 40, 75–78 (1973)
Katriňák T., Mederly P.: Construction of modular p-algebras. Algebra Universalis 4, 301–315 (1974)
Author information
Authors and Affiliations
Corresponding author
Additional information
Presented by M. Ploščica.
While working on this paper, the authors were supported by VEGA Grant No. 1/0588/09 of the Slovak Republic.
Rights and permissions
About this article
Cite this article
Katriňák, T., Guričan, J. Finite pseudocomplemented lattices: The spectra and the Glivenko congruence. Algebra Univers. 66, 151 (2011). https://doi.org/10.1007/s00012-011-0145-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00012-011-0145-0