Hardcover ISBN:  9781470414931 
Product Code:  HMATH/41 
441 pp 
List Price:  $115.00 
MAA Member Price:  $103.50 
AMS Member Price:  $92.00 
Electronic ISBN:  9781470417178 
Product Code:  HMATH/41.E 
441 pp 
List Price:  $109.00 
MAA Member Price:  $98.10 
AMS Member Price:  $87.20 

Book DetailsHistory of MathematicsVolume: 41; 2014MSC: Primary 01; 20;
The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a fullfledged theory.
Semigroup theory might be termed ‘Cold War mathematics’ because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in East and West, and the study of the extent to which contact between the two sides was possible.ReadershipGraduate students and research mathematicians interested in algebraic semigroups and the history of mathematics during the Cold War.

Table of Contents

Chapters

Algebra at the beginning of the twentieth century

Communication between East and West

Anton Kazimirovich Sushkevich

Unique factorisation in semigroups

Embedding semigroups in groups

The Rees Theorem

The French school of ’demigroupes’

The expansion of the theory in the 1940s and 1950s

The postSushkevich Soviet school

The development of inverse semigroups

Matrix representations of semigroups

Books, seminars, conferences, and journals

Basic theory


Additional Material

Reviews

The book is very readable, and both nonexperts and experts may find it interesting. The former can see the book as a case study of how a new area of mathematics can grow from a handful of more or less independently working mathematicians to a truly international, collaborative community, despite the difficulties of communication across the Iron Curtain...For experts, a comprehensive study of the early years of semigroup theory might shed light on some previously unnoticed connections between different branches of semigroup theory or between semigroup theory and other parts of mathematics.
Miklós Hartmann, ACTA Sci. Math. 
This detailed study of the history of semigroup theory is an important contribution both to the history of algebra in the 20th century and to the history of the relations between mathematicians working on both sides of the Iron Curtain.
S.C. Coutinho, Mathematical Gazette 
The book itself is a mixture of history and of mathematics throughout. Although the emphasis is squarely on the mathematics, there are biographies of key figures, explaining who these people were along with the occasional anecdote about their mathematical lives, reflecting their characters. For example, Lyapin was not one of the original editors of Semigroup Forum because the Soviet authorities refused him permission. ...Overall, this is valuable reference work, detailing much of the history of algebraic semigroups that might otherwise be lost. For connoisseurs of the subject, it represents a really good read.
Mathematical Reviews 
Hollings has done a masterful job. The book is well written, both in telling the story and in explaining the mathematics involved. It is an important and valuable contribution to the history of mathematics in the 20th century. This book should be in the libraries of all research institutions, and on the shelves of those interested in the history of abstract algebra, as well as those of semigroup researchers.
MAA Reviews


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 Book Details
 Table of Contents
 Additional Material
 Reviews

 Request Review Copy
The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a fullfledged theory.
Semigroup theory might be termed ‘Cold War mathematics’ because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in East and West, and the study of the extent to which contact between the two sides was possible.
Graduate students and research mathematicians interested in algebraic semigroups and the history of mathematics during the Cold War.

Chapters

Algebra at the beginning of the twentieth century

Communication between East and West

Anton Kazimirovich Sushkevich

Unique factorisation in semigroups

Embedding semigroups in groups

The Rees Theorem

The French school of ’demigroupes’

The expansion of the theory in the 1940s and 1950s

The postSushkevich Soviet school

The development of inverse semigroups

Matrix representations of semigroups

Books, seminars, conferences, and journals

Basic theory

The book is very readable, and both nonexperts and experts may find it interesting. The former can see the book as a case study of how a new area of mathematics can grow from a handful of more or less independently working mathematicians to a truly international, collaborative community, despite the difficulties of communication across the Iron Curtain...For experts, a comprehensive study of the early years of semigroup theory might shed light on some previously unnoticed connections between different branches of semigroup theory or between semigroup theory and other parts of mathematics.
Miklós Hartmann, ACTA Sci. Math. 
This detailed study of the history of semigroup theory is an important contribution both to the history of algebra in the 20th century and to the history of the relations between mathematicians working on both sides of the Iron Curtain.
S.C. Coutinho, Mathematical Gazette 
The book itself is a mixture of history and of mathematics throughout. Although the emphasis is squarely on the mathematics, there are biographies of key figures, explaining who these people were along with the occasional anecdote about their mathematical lives, reflecting their characters. For example, Lyapin was not one of the original editors of Semigroup Forum because the Soviet authorities refused him permission. ...Overall, this is valuable reference work, detailing much of the history of algebraic semigroups that might otherwise be lost. For connoisseurs of the subject, it represents a really good read.
Mathematical Reviews 
Hollings has done a masterful job. The book is well written, both in telling the story and in explaining the mathematics involved. It is an important and valuable contribution to the history of mathematics in the 20th century. This book should be in the libraries of all research institutions, and on the shelves of those interested in the history of abstract algebra, as well as those of semigroup researchers.
MAA Reviews