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Almost distributive lattices

Part of: Boolean algebras (Boolean rings) Distributive lattices

Published online by Cambridge University Press:  09 April 2009

U. Maddana Swamy  and
G. C. Rao
U. Maddana Swamy
Affiliation:
Department of Mathematics, Andhra University, Waltair-530 003, India
G. C. Rao
Affiliation:
Department of Mathematics, Andhra University, Waltair-530 003, India
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Abstract

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The concept of ‘Almost Distributive Lattices’ (ADL) is introduced. This class of ADLs includes almost all the existing ring theoretic generalisations of a Boolean ring (algebra) like regular rings, P-rings, biregular rings, associate rings, P1-rings, triple systems, etc. This class also includes the class of Baer-Stone semigroups. A one-to-one correspondence is exhibited between the class of relatively complemented ADLs and the class of Almost Boolean Rings analogous to the well-known Stone's correspondence. Many concepts in distributive lattices can be extended to the class of ADLs through its principal ideals which from a distributive lattice with 0. Subdirect and Sheaf representations of an ADL are obtained.

MSC classification

Secondary: 06D99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 1 , June 1981 , pp. 77 - 91
Copyright
Copyright © Australian Mathematical Society 1981

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