International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 461-476
doi:10.1155/S0161171280000348
Representation of certain classes of distributive lattices by sections of sheaves
Mathematics Department, Andhra University, Waltair 530 003, India
Received 13 March 1979; Revised 9 July 1979
Copyright © 1980 U. Maddana Swamy and P. Manikyamba. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Epstein and Horn ([6]) proved that a Post algebra is always a P-algebra and in a P-algebra, prime ideals lie in disjoint maximal chains. In this paper it is shown that a P-algebra L is a Post algebra of order n≥2, if the prime ideals of L lie in disjoint maximal chains each with n−1 elements. The main tool used in this paper is that every bounded distributive lattice is isomorphic with the lattice of all global sections of a sheaf of bounded distributive lattices over a Boolean space. Also some properties of P-algebras are characterized in terms of the stalks.