# 半群

## 定义

### 相关概念

• 幺半群独异点

• 嵌入

$\bullet$ 交换半群可以嵌入到群中当且仅当它有消除性质

## 历史

Anton Suschkewitsch 经常被归功获得了关于半群的第一个非平凡的结果。他1928年的论文《Über die endlichen Gruppen ohne das Gesetz der eindeutigen Umkehrbarkeit》(《关于没有唯一可逆性规则的有限群》) 确定了有限简单半群的结构并证明了有限半群的极小理想(或Green关系 J-类)是简单的[2]。在这个基点之上，半群理论的基础进一步由 David ReesJames Alexander GreenEvgenii Sergeevich LyapinAlfred H. CliffordGordon Preston 建立。后面二人在 1961 年出版了半群理论的专论。

## 引用

• John M. Howie is the author of two books, published twenty years apart, which are often cited as a basic reference in the mathematical community.
• Two volumes of Samuel Eilenberg have also been a common reference for the applications of semigroup theory in theoretical computer science.
• The algebraic theory of semigroups, A. H. Clifford and G. B. Preston. American Mathematical Society, 1961 (volume 1), 1967 (volume 2).
• Semigroups: an introduction to the structure theory, Pierre Antoine Grillet. Marcel Dekker, Inc., 1995.
• Semigroup Forum is the best-known periodical devoted specifically to the subject of semigroups.

## 注释

1. ^ http://web.archive.org/19991003231318/members.aol.com/jeff570/s.html Earliest Known Uses of Some of the Words of Mathematics
2. ^ 2.0 2.1 http://www-users.york.ac.uk/~cdh500/suschkewitsch3.pdf An account of Suschkewitsch's paper by Christopher Hollings
3. ^ Varieties of Formal Languages, J.É. Pin, Plenum Press, 1986.