Hardcover ISBN:  9780821804957 
Product Code:  SURV/45 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412760 
Product Code:  SURV/45.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821804957 
eBook: ISBN:  9781470412760 
Product Code:  SURV/45.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 
Hardcover ISBN:  9780821804957 
Product Code:  SURV/45 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412760 
Product Code:  SURV/45.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821804957 
eBook ISBN:  9781470412760 
Product Code:  SURV/45.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 45; 1996; 388 ppMSC: Primary 16; 17; 18; Secondary 08; 13; 14
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 strived—and succeeded—in creating a volume that is very userfriendly.
ReadershipGraduate students and research mathematicians interested in algebra, ring theory, and algebraic geometry.

Table of Contents

Chapters

I. Introduction

II. Review of coalgebras and representable functors

III. Representable functors from rings to abelian groups

IV. Digressions on semigroups, etc.

V. Representable functors from algebras over a field to rings

VI. Representable functors from $k$rings to rings

VII. Representable functors from rings to general groups and semigroups

VIII. Representable functors on categories of commutative associative algebras

IX. Representable functors on categories of Lie algebras

X. Multilinear algebra of representable functors on $k\mathrm {Ring}^1$

XI. Directions for further investigation


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


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Reviews
 Requests
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 strived—and succeeded—in creating a volume that is very userfriendly.
Graduate students and research mathematicians interested in algebra, ring theory, and algebraic geometry.

Chapters

I. Introduction

II. Review of coalgebras and representable functors

III. Representable functors from rings to abelian groups

IV. Digressions on semigroups, etc.

V. Representable functors from algebras over a field to rings

VI. Representable functors from $k$rings to rings

VII. Representable functors from rings to general groups and semigroups

VIII. Representable functors on categories of commutative associative algebras

IX. Representable functors on categories of Lie algebras

X. Multilinear algebra of representable functors on $k\mathrm {Ring}^1$

XI. Directions for further investigation

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