Description 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.
Audience
Researchers, students, and professionals working in both pure and applied mathematics
Contents 1.) Linear algebra. Fields. Algebraic number theory
2.) Category theory. Homological and homotopical algebra
3.) Commutative and associative
rings and algebras
4.) Other algebraic structures. Nonassociative rings and algebras. Commutative and associative rings and algebras
with additional structure.
5.) Groups and semigroups
6.) Representations and invariant theory
7.) Machine computation. Algorithms. Tables
8.) Applied algebra
9.) History of algebra
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