**History of Mathematics**

Volume: 41;
2014;
441 pp;
Hardcover

MSC: Primary 01; 20;

Print ISBN: 978-1-4704-1493-1

Product Code: HMATH/41

List Price: $109.00

AMS Member Price: $87.20

MAA member Price: $98.10

**Electronic ISBN: 978-1-4704-1717-8
Product Code: HMATH/41.E**

List Price: $109.00

AMS Member Price: $87.20

MAA member Price: $98.10

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#### Supplemental Materials

# Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups

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*Christopher Hollings*

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 full-fledged 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.

#### Readership

Graduate students and research mathematicians interested in algebraic semi-groups and the history of mathematics during the Cold War.

#### Reviews & Endorsements

The book is very readable, and both non-experts 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

#### Table of Contents

# Table of Contents

## Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Algebra at the beginning of the twentieth century 114
- Communication between East and West 1124
- Anton Kazimirovich Sushkevich 4558
- Unique factorisation in semigroups 7790
- Embedding semigroups in groups 107120
- The Rees Theorem 135148
- The French school of ’demi-groupes’ 161174
- The expansion of the theory in the 1940s and 1950s 183196
- The post-Sushkevich Soviet school 217230
- The development of inverse semigroups 249262
- Matrix representations of semigroups 277290
- Books, seminars, conferences, and journals 303316
- Basic theory 333346
- Notes 337350
- Bibliography 373386
- Name index 429442
- Subject index 433446
- Back Cover Back Cover1457