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Representation of certain classes of distributive lattices by sections of sheaves

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  • U. Maddana Swamy
  • P. Manikyamba

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.

Suggested Citation

  • U. Maddana Swamy & P. Manikyamba, 1980. "Representation of certain classes of distributive lattices by sections of sheaves," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 3, pages 1-16, January.
    • Handle: RePEc:hin:jijmms:456093
    DOI: 10.1155/S0161171280000348
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