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...
Αποθηκεύτηκε σε:
| Κύριος συγγραφέας: | |
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| Μορφή: | Livre numérique |
| Γλώσσα: | Anglais |
| Έκδοση: |
Boston, MA :
Birkhäuser Boston
2012.
Cham : Springer Nature |
| Θέματα: | |
| Διαθέσιμο Online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Σημείωση: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Sheaves of algebras over Boolean spaces, Arthur Knoebel, [Basel], Birkhäuser, Springer Science+Business Media, 2012, 1 vol. (XII-329 p.), 978-0-8176-4218-1 |
| Περίληψη: | 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 |
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| Περιγραφή τεκμηρίου: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9780817646424 |
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