Sheaves from Factor Congruences

Arthur Knoebel ()

Chapter VI in Sheaves of Algebras over Boolean Spaces, 2012, pp 147-178 from Springer

Abstract: Abstract 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.

Keywords: Prime Ideal; Boolean Algebra; Global Section; Factor Object; Factor Element (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-0-8176-4642-4_6

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