Representation of certain classes of distributive lattices by sections of sheaves

• Main Authors: U. Maddana Swamy, P. Manikyamba
• Format: Article
• Language: English
• Published: Hindawi Limited 1980-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Subjects: post algebra; P-algebra; B-algebra; Heyting algebra; Stone lattice; boolean space; sheaf of distributive lattices over a boolean space; prime ideals lie in disjoint maximal chains; regular chain base.
• Online Access: http://dx.doi.org/10.1155/S0161171280000348

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.