Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups
About this Title
Publication: History of Mathematics
Publication Year: 2014; Volume 41
ISBNs: 978-1-4704-1493-1 (print); 978-1-4704-1717-8 (online)
MathSciNet review: MR3222721
MSC: Primary 20-03; Secondary 01A60, 20Mxx
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.
Table of Contents
- 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