Ebook: The Concise Handbook of Algebra
- Tags: Algebra, Field Theory and Polynomials, Commutative Rings and Algebras, Associative Rings and Algebras, Non-associative Rings and Algebras
- Year: 2002
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.
Content:
Front Matter....Pages i-xvi
Semigroups....Pages 1-70
Groups....Pages 71-151
Rings, Modules, Algebras....Pages 153-354
Fields....Pages 355-381
Representation Theory....Pages 383-415
Lattices....Pages 417-450
Universal Algebra....Pages 451-490
Homological Algebra....Pages 491-522
Miscellaneous....Pages 523-542
Back Matter....Pages 543-618
Content:
Front Matter....Pages i-xvi
Semigroups....Pages 1-70
Groups....Pages 71-151
Rings, Modules, Algebras....Pages 153-354
Fields....Pages 355-381
Representation Theory....Pages 383-415
Lattices....Pages 417-450
Universal Algebra....Pages 451-490
Homological Algebra....Pages 491-522
Miscellaneous....Pages 523-542
Back Matter....Pages 543-618
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