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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A sheaf representation of distributive pseudocomplemented lattices


Author: William H. Cornish
Journal: Proc. Amer. Math. Soc. 57 (1976), 11-15
MSC: Primary 06A23
MathSciNet review: 0424630
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Abstract: The main result of this paper shows that a distributive pseudocomplemented lattice $ (L; \vee , \wedge {,^ \ast },0,1)$, considered as an algebra of type $ \langle 2,2,1,0,0\rangle $, can be represented as the algebra of all global sections in a certain sheaf. The stalks are the quotient algebras $ L/\Theta (O(P))$, where $ P$ is a prime ideal in $ L$. The base space is the set of prime ideals of $ L$ equipped with the topology whose basic open sets are of the form $ P:P$ prime in $ L,{x^{ \ast \ast }} \notin P$ for some $ x \in L$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0424630-2
PII: S 0002-9939(1976)0424630-2
Keywords: Distributive pseudocomplemented lattice, sheaf representation, $ \alpha $-ideal, congruences
Article copyright: © Copyright 1976 American Mathematical Society