Boolean Subsemilattices

  • Arthur Knoebel


Ever since Stone represented Boolean algebras topologically [Stone36], many have extended his theorem to diverse algebraic systems. Structurally, it suffices to discover a fragment of the congruence lattice that is Boolean. The value of such a fragment, to be called a Boolean subsemilattice in the first section, is flexibility. By varying the Boolean subsemilattice to suit the context, different representation theorems follow automatically. In a later chapter, for example, by looking at all the factor ideals of a unital ring in which the annihilator of any element is a principal ideal generated by an idempotent, we obtain stalks with no zero divisors. With sheaves this theorem can be extended well beyond ring theory.


Prime Ideal Boolean Algebra Base Space Global Section Congruence Lattice 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.AlbuquerqueUSA

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