Arthur Knoebel

Sheaves of Algebras over Boolean Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 331
• Erscheinungstermin: 16. Dezember 2011
• Englisch
• ISBN-13: 9780817646424
• Artikelnr.: 37340607

Inhaltsangabe

From the contents:
- 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.

Rezensionen

From the reviews:

"This monograph adapts the intuitive idea of a metric space to universal algebra, leading to the useful device of a complex, from which a sheaf is constructed directly. The gist of the author's ideas is that one need not look at all congruences of an algebra, but at only some of them comprising a Boolean subsemilattice of congruences ... . As for prerequisites, the reader should have a nodding acquaintance with universal algebra, logic, categories, topology, and Boolean algebra." (Hirokazu Nishimura, Zentralblatt MATH, Vol. 1243, 2012)

"This book brings together investigations that span several decades by the author and others into how in general one can obtain a representation of arbitrary algebras by sheaves over Boolean spaces. ... The book is well written and contains extensive references. ... Exercises and open problems are liberally interspersed throughout the monograph. It is recommended for anyone with an interest in the decomposition of general algebras primarily from the viewpoint of the universal algebra." (S. Comer, Mathematical Reviews, January, 2013)