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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
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Abstract

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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

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