Handbook of Algebra

by M. Hazewinkel (Editor)

Overview

Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest.

In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc.

The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published.

A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.

Product Details

ISBN-13:	9780444532572
Publisher:	Elsevier Science
Publication date:	07/18/2009
Series:	Handbook of Algebra , #6
Pages:	592
Product dimensions:	6.10(w) x 9.00(h) x 1.20(d)

Table of Contents

Preface     v
Outline of the Series     ix
List of Contributors     xxiii
Fields, Galois Theory, and Algebraic Number Theory     1
From field theoretic to abstract co-Galois theory   T. Albu     3
Category Theory     85
Operads and PROPs   M. Markl     87
Homological Algebra. Cohomology. Cohomological Methods in Algebra. Homotopical Algebra     141
A[subscript infinity]-algebras, A[subscript infinity]-categories, and A[subscript infinity]-functors   V. Lyubashenko   O. Manzyuk     143
0-Cohomology of semigroups   B.V. Novikov     189
Associative Rings and Algebras     211
Finite rings with applications   A.A. Nechaev     213
Lattices and Partially Ordered Sets     321
Algebraic and categorical aspects of quantales   D. Kruml   J. Paseka     323
Hopf Algebras and Related Structures     363
Hopf algebras in renormalisation   D. Manchon     365
Classification of semisimple Hopf algebras   A. Masuoka     429
Machine Computation. Algorithms. Tables. Counting Algebraic Structures     457
Integral representation and algorithms for closed formsummation   G.P. Egorychev   E.V. Zima     459
Subject Index     531

What People are Saying About This

From the Publisher

The Handbook of Algebra provides a convenient, thorough, and practical source of information for students, academics, and professionals.

Editorial Reviews

.."...This is obviously the kind of book one consults when detailed information about a specific topic is wanted and it will be splendid to have it all brought together in a single series once the handbook is complete."

..".an excellent index is included which will help a mathematician working in an area other than his own to find sufficient information on the topic in question."

From the Publisher