Handbook of Algebra, Volume Volume 1

Algebra, as we know it today, consists of many different ideas, concepts and results. Estimates 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. 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 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 first volume articles from three 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.