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

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Hardcover ISBN: 978-1-4704-1493-1
Product Code: HMATH/41
441 pp
List Price: $115.00 MAA Member Price:$103.50
AMS Member Price: $92.00 Electronic ISBN: 978-1-4704-1717-8 Product Code: HMATH/41.E 441 pp List Price:$109.00
MAA Member Price: $98.10 AMS Member Price:$87.20
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List Price: $172.50 MAA Member Price:$155.25
AMS Member Price: $138.00 Click above image for expanded view Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups Available Formats:  Hardcover ISBN: 978-1-4704-1493-1 Product Code: HMATH/41 441 pp  List Price:$115.00 MAA Member Price: $103.50 AMS Member Price:$92.00
 Electronic ISBN: 978-1-4704-1717-8 Product Code: HMATH/41.E 441 pp
 List Price: $109.00 MAA Member Price:$98.10 AMS Member Price: $87.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$172.50
MAA Member Price: $155.25 AMS Member Price:$138.00
• Book Details

History of Mathematics
Volume: 412014
MSC: 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 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.

Graduate students and research mathematicians interested in algebraic semi-groups 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 ’demi-groupes’
• The expansion of the theory in the 1940s and 1950s
• The post-Sushkevich Soviet school
• The development of inverse semigroups
• Matrix representations of semigroups
• Books, seminars, conferences, and journals
• Basic theory

• Reviews

• 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
• Request Review Copy
Volume: 412014
MSC: 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 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.

Graduate students and research mathematicians interested in algebraic semi-groups 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 ’demi-groupes’
• The expansion of the theory in the 1940s and 1950s
• The post-Sushkevich 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 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
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