Sheaves of Algebras over Boolean Spaces [Hardcover]

This unique monograph building bridges among a number of different areas of mathematics such as algebra, topology, and category theory. The author uses various tools to develop new applications of classical concepts. Detailed proofs are given for all major theorems,?about half?of which are completely new.

Sheaves of Algebras over Boolean Spaces will take readers on a journey through sheaf theory, an important part of universal algebra. This excellent reference text is suitable for graduate students, researchers, and those who wish to learn about sheaves of algebras.

Sheaves of Algebras over Boolean Spaces takes the reader on a journey through sheaf theory. The coverage builds bridges spanning algebra, topology, and category theory and revealing new connections between classical algebra and universal algebra.

Sheaves of Algebras over Boolean Spaces comprehensively covers sheaf theory as applied to universal algebra. Sheaves decompose general algebras into simpler pieces called the stalks. A classical case is commutative von Neumann regular rings, whose stalks are fields. Other classical theorems also extend to shells, a common generalization of rings and lattices.

This text presents intuitive ideas from topology such as the notion of metric space and the concept of central idempotent from ring theory. These lead to the abstract notions of complex and factor element, respectively. Factor elements are defined by identities, discovered for shells for the first time, explaining why central elements in rings and lattices have their particular form. Categorical formulations of the many representations by sheaves begin with adjunctions and move to equivalences as the book progresses, generalizing Stones theorem for Boolean algebras.

Half of the theorems provided in the text are new; the rest are presented in a coherent lӴ