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Cogroups and Co-rings in Categories of Associative Rings
George M. Bergman, University of California, Berkeley, CA, and Adam O. Hausknecht, University of Massachusetts at Darmouth, Dartmouth, MA

Mathematical Surveys and Monographs
1996; 388 pp; hardcover
Volume: 45
ISBN-10: 0-8218-0495-2
ISBN-13: 978-0-8218-0495-7
List Price: US$96
Member Price: US$76.80
Order Code: SURV/45
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This book studies representable functors among well-known 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 strived--and succeeded--in creating a volume that is very user-friendly.


Graduate students and research mathematicians interested in algebra, ring theory, and algebraic geometry.


"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 well-known 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
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