The Concise Handbook of Algebra

1. Front Matter

   Pages i-xvi

   PDF

2. Semigroups

   • Lev N. Shevrin, Peter M. Higgins, Nik Ruškuc, Jorge Almeida, Peter G. Trotter, John M. Howie et al.

   Pages 1-70

3. Groups

   • Alexander V. Mikhalev, Charles R. Leedham-Green, Hans Lausch, Peter J. Cameron, Joachim Hilgert, Peter J. Olver et al.

   Pages 71-151

4. Rings, Modules, Algebras

   • Robert Gilmer, Joachim von zur Gathen, David F. Anderson, Marco Fontana, Ira J. Papick, T. Y. Lam et al.

   Pages 153-354

5. Fields

   • Shreeram S. Abhyankar, Harald Niederreiter, Joseph J. Rotman, Andy R. Magid, A. V. Mikhalev, E. V. Pankratiev et al.

   Pages 355-381

6. Representation Theory

   • Donald S. Passman, I. Martin Isaacs, Albert Fässler, Peter Fleischmann, Joachim Hilgert, Kenichi Kanatani et al.

   Pages 383-415

7. Lattices

   • George Grätzer, E. Tamás Schmidt, Ralph Freese, Viacheslav N. Saliĭ, Gudrun Kalmbach, Carlton J. Maxson et al.

   Pages 417-450

8. Universal Algebra

   • Vyacheslav A. Artamonov, Günter F. Pilz, Boris I. Plotkin, Kalle Kaarli, Lev N. Shevrin, Evgeny V. Sukhanov et al.

   Pages 451-490

9. Homological Algebra

   • Peter Hilton, Yefim Katsov, Sarah Glaz, Alexander V. Mikhalev, Askar A. Tuganbaev, Jonathan M. Rosenberg

   Pages 491-522

10. Miscellaneous

    • H. Jerome Keisler, Günter F. Pilz, V. T. Markov, A. V. Mikhalev, A. A. Nechaev, Hans Kaiser

    Pages 523-542

11. Back Matter

    Pages 543-618

    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.

• Abelian group
• Group theory
• Lattice
• Permutation
• Representation theory
• algebra

• Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia

  Alexander V. Mikhalev

• Institute of Algebra, Johannes Kepler University-Linz, Linz, Austria

  Günter F. Pilz

Policies and ethics