Algebra, as we know it today, consists of many different ideas, concepts and results. An estimate of the number of these different "items" would be between 50,000 and 200,000. Many of these have been named and many more could have a "name" or a convenient designation. Even the non-specialist 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. This handbook is designed to supply the necessary information in any of these cases. In addition to the primary information given in the handbook, there are references to relevant articles, books or lecture notes to help the reader. A particularly important function of the book 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.
Rezensionen / Stimmen
"Monatshefte fur Mathematik, H. Mitsch, 1998; "...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." Ultramicroscopy, Vol. 87, 2001; "........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.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Elsevier Science & Technology
Zielgruppe
ISBN-13
978-0-444-51264-2 (9780444512642)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Preface.
Outline of the Series.
List of Contributors.
Section 1A. Linear Algebra
Linear algebra over commutative rings (J.A. Hermida-Alonso).
Correction to the chapter in Volume 1, Matrix functions (L. Rodman).
Section 2A. Category Theory.
Monads of sets (E. Manes).
Section 2C. Algebraic K-theory.
Classical algebraic K-theory: the functors (A. Kuku).
Section 2D. Model Theoretic Algebra.
(see also Paul C. Eklof, Whitehead modules in section 3B)
Model theory for algebra (M. Prest).
Model theory and modules (M. Prest).
Section 3A. Commutative Rings and Algebras.
Monomial algebras and polyhedral geometry (R.H. Villareal).
Section 3B. Associative Rings and Algebras.
Whitehead modules (P.C. Eklof).
Flat covers (E.E. Enochs).
The Krull-Schmidt theorem (A. Facchini).
Coherent rings and annihilator conditions in matrix and polynomial rings (C. Faith).
Hamilton's quaternions (T.Y. Lam).
Group rings (S.K. Sehgal).
Semiregular, weakly regular and &pgr;-regular rings (A.A. Tuganbaev).
Max rings and V-rings (A.A. Tuganbaev).
Section 3C. Co-algebras.
Co-algebras (W. Michaelis).
Section 4A. Lattrices and Partially Ordered Sets.
Frames (A. Pultr).
Section 4D. Varieties of Algebras, Groups, ...
Quasivarieties (V.A. Artamonov).
Section 4E. Lie Algebras.
Free lie algebras (C. Reutenauer).
Section 4H. Rings and Algebras with Additional Structure.
Yangians and their applications (A.I. Molev).
Lambda-rings (F. Patras).
Section 5A. Groups and Semigroups.
Branch groups (L. Bartholdi. R. Grigorchuk. Z. Sunik).
Index.
