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| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20140310151441.0 |
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111215s2012 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780817646424 |
|
978-0-8176-4642-4 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA150-272 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
Boston, MA : |
| -- |
Birkhäuser Boston : |
| -- |
Imprint: Birkhäuser, |
| -- |
2012. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Knoebel, Arthur. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Sheaves of Algebras over Boolean Spaces |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Arthur Knoebel. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XII, 331p. 63 illus. |
| Other physical details |
online resource. |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
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 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
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 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Algebra. |
|
|---|
| Topical term or geographic name as entry element |
Topology. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Algebra. |
|
|---|
| Topical term or geographic name as entry element |
Topology. |
|
|---|
| Topical term or geographic name as entry element |
Category Theory, Homological Algebra. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9780817642181 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-0-8176-4642-4 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
