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Prime ideal characterization of chain based lattices

Part of: Distributive lattices Categories and geometry Boolean algebras (Boolean rings)

Published online by Cambridge University Press:  09 April 2009

U. Maddna Swamy ,
G. C. Rao  and
P. Manikyamba
U. Maddna Swamy
Affiliation:
Department of Mathematics, Andhra University,, Waltair-530003, India
G. C. Rao
Affiliation:
Department of Mathematics, Andhra University,, Waltair-530003, India
P. Manikyamba
Affiliation:
Department of Mathematics, Andhra University,, Waltair-530003, India
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Abstract

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Epstein and Horn, in their paper ‘Chain based lattices’, characterized P1-lattices, and P2-lattices in terms of their prime ideals. But no such prime ideal characterization for P0-lattices was given. Our main aim in this paper is to characterize P0-lattices in terms of their prime ideals. We also give a necessary and sufficient condition for a P-algebra to be a P0-lattice (and hence a P2-lattice).

Keywords

B-normal latticesP-algebrachain based latticessheaf of bounded distributive latticescontinuity axiomP(L) is determined by a subset of L.

MSC classification

Secondary: 06D99: None of the above, but in this section 18F20: Presheaves and sheaves
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 1 , September 1980 , pp. 98 - 106
Copyright
Copyright © Australian Mathematical Society 1980

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