Sheaves from Factor Congruences



Factor congruences come from the product decompositions of an algebra. Using only them, rather than arbitrary congruences, creates a sheaf such that the algebra is isomorphic to the algebra of all global sections of the sheaf, not just to a subalgebra, as in the last chapter.The first section studies when there is a Boolean lattice of some of the factor congruences, and the third restricts attention to where all the factor congruences form a Boolean algebra.In between, many ways to identify algebras with Boolean lattices of factor congruences are found.The chapter closes with categorical equivalences between these classes of algebras and their sheaves.


Prime Ideal Boolean Algebra Global Section Factor Object Factor Element 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.AlbuquerqueUSA

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