Boolean Lattices, Rings and the Equivalence of Categories

Abstract

This thesis is concerned With showing the relations among Boolean lattices, Boolean rings and Boolean spaces, It establishes that the categories of Boolean lattices and proper Boolean lattice homomorphisms, Boolean spaces and proper continuous maps, Boolean rings and proper ring homomorphisms are equivalent to each other, In the final chapter the notion of a Boolean semi-group is used to obtain an alternate characterization of a Boolean lattice.