Mathematical Surveys and Monographs 1996; 388 pp; hardcover Volume: 45 ISBN10: 0821804952 ISBN13: 9780821804957 List Price: US$101 Member Price: US$80.80 Order Code: SURV/45
 This book studies representable functors among wellknown varieties of algebras. All such functors from associative rings over a fixed ring \(R\) to each of the categories of abelian groups, associative rings, Lie rings, and to several others are determined. Results are also obtained on representable functors on varieties of groups, semigroups, commutative rings, and Lie algebras. The book includes a "Symbol index", which serves as a glossary of symbols used and a list of the pages where the topics so symbolized are treated, and a "Word and phrase index". The authors have strivedand succeededin creating a volume that is very userfriendly. Readership Graduate students and research mathematicians interested in algebra, ring theory, and algebraic geometry. Reviews "Indisputably, Bergman and Hausknecht have done a remarkable job of surveying a broad range of territories ... There is no comparable book, or more technically, no book substitutable in significant part for this one. The dedicated reader will soon find herself in love with the very full indexing ..."  Bulletin of the AMS "Constitutes a hefty contribution to the study of coalgebras and representable funtors on wellknown varieties of algebras."  Zentralblatt MATH "Very elegantly written."  Mathematical Reviews "This book is fascinating in many aspects: First, its rigorous, systematic and accessible exposition of the subject makes it a bright landmark at the crossroads of arithmetic and mathematical physics; no doubt it will become a basic reference in random matrix theory. Second, it offers its reader a bouquet of beautiful new results but also leaves the door open to many challenging conjectures. The book will constitute, for those working in the field of \(L\)functions, a major source of inspiration for the next decades."  Mathematical Reviews Featured Review Table of Contents  Introduction
 Review of coalgebras and representable functors
 Representable functors from rings to abelian groups
 Digressions on semigroups, etc.
 Representable functors from algebras over a field to rings
 Representable functors from \(k\)rings to rings
 Representable functors from rings to general groups and semigroups
 Representable functors on categories of commutative associative algebras
 Representable functors on categories of Lie algebras
 Multilinear algebra of representable functors on \(k\)Ring\(^1\)
 Directions for further investigation
 References
 Word and phrase index
 Symbol index
