Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T09:39:36.939Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on subdirectly irreducible distributive double p-algebras

Part of: Distributive lattices Boolean algebras (Boolean rings)

Published online by Cambridge University Press:  09 April 2009

M. E. Adams  and
T. Katriňák
M. E. Adams
Affiliation:
Department of MathematicsState University of New YorkNew Paltz, New York, U.S.A.
T. Katriňák
Affiliation:
Katedra algebry a teórie číselMatematicko-fyzikálna fakultaUniversity KomenskéhoBratislava Czechoslovakia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A regular double p-algebra L satisfying (i) ∩(xn(+*); n < ω) for every 1 ≠ x ∈ L and (ii) L is not subdirectly irreducible, is constructed. The construction is purely topological and the desired result is obtained via the known Priestly duality. The notion of an auxiliary regular double p-algebra is introduced and the algebras having this property are characterized.

MSC classification

Secondary: 06D15: Pseudocomplemented lattices 06E15: Stone spaces (Boolean spaces) and related structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 1 , August 1983 , pp. 46 - 58
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Beazer, R., ‘The determination congruence on double p-algebras’, Algebra Universalis 6 (1976), 121–129.CrossRefGoogle Scholar
[2]Beazer, R., ‘Subdirectly irreducible double Heyting algebras’, Algebra Universalis 10 (1980), 220–224.CrossRefGoogle Scholar
[3]Beazer, R., ‘Finitely subdirectly irreducible algebras with pseudocomplementation’, Algebra Universalis 12 (1981), 376–386.CrossRefGoogle Scholar
[4]Davey, B. A., ‘Subdirectly irreducible distributive double p-algebras’, Algebra Universalis, 8 (1978), 73–88.CrossRefGoogle Scholar
[5]Grätzer, G., General Lattice Theory (Birkhäuser Verlag, Basel, 1978).CrossRefGoogle Scholar
[6]Katriňák, T., ‘Construction of regular double p-algebras’, Bull. Soc. Roy. Sci. Liège 43 (1974), 294–301.Google Scholar
[7]Katriňák, T., ‘Subdirectly irreducible distributive double p-algebras’, Algebra Universalis 10 (1980), 195–219.CrossRefGoogle Scholar
[8]Kelley, J. L., ‘General Topology (Van Nostrand Reinhold, New York, 1955).Google Scholar
[9]Priestley, H. A., ‘The construction of spaces dual to pseudocomplemented distributive lattices’, Quart J. Math. Oxford Ser. (2) 26 (1975), 215–228.CrossRefGoogle Scholar