Sheaves of Algebras over Boolean Spaces

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 ext...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Knoebel, Arthur (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
Edición:1st ed. 2012.
Temas:
Algebra.
Topology.
Algebra, Homological.
Category Theory, Homological Algebra.
Acceso en línea:Texto Completo

MARC

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100 1 |a Knoebel, Arthur.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Sheaves of Algebras over Boolean Spaces  |h [electronic resource] /  |c by Arthur Knoebel. 
250 |a 1st ed. 2012. 
264 1 |a Boston, MA :  |b Birkhäuser Boston :  |b Imprint: Birkhäuser,  |c 2012. 
300 |a XII, 331 p. 63 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
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505 0 |a Preface -- Introduction -- Algebra -- Tools -- Complexes and their Sheaves -- Boolean Subsemilattices -- Sheaves from Factor Congruences -- Shells -- Baer-Stone Shells -- Strict Shells -- Varieties Generated by Preprimal Algebras -- Return to General Algebras -- Further Examples Pointing to Future Research -- List of Symbols -- References -- Index. 
520 |a 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 Stone's theorem for Boolean algebras. Half of the theorems provided in the text are new; the rest are presented in a coherent framework, starting with the most general, and proceeding to specific applications. Many open problems and research areas are outlined, including a final chapter summarizing applications of sheaves in diverse fields that were not covered earlier in the book. This monograph is suitable for graduate students and researchers, and it will serve as an excellent reference text for those who wish to learn about sheaves of algebras. 
650 0 |a Algebra. 
650 0 |a Topology. 
650 0 |a Algebra, Homological. 
650 1 4 |a Algebra. 
650 2 4 |a Topology. 
650 2 4 |a Category Theory, Homological Algebra. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9780817671679 
776 0 8 |i Printed edition:  |z 9780817642181 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-0-8176-4642-4  |z Texto Completo 
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912 |a ZDB-2-SXMS 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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