inverse semigroup
English
Noun
inverse semigroup (plural inverse semigroups)
- (algebra, group theory) A semigroup in which every element x has an inverse y, such that x = xyx and y = yxy.
- 2002, Peter G. Trotter, A.9: Regular Semigroups, Aleksandr Vasilʹevich Mikhalev, Günter Pilz (editors), The Concise Handbook of Algebra, page 35,
- Examples of regular semigroups include any band, inverse semigroup or completely regular semigroup (see sections A. 2, A. 11, and A. 10); in particular, any group is a regular semigroup.
- 2008, Olexandr Ganyushkin; Volodymyr Mazorchuk, Classical Finite Transformation Semigroups: An Introduction, page v:
- Inverse semigroups form a class of semigroups which are closest (in some sense) to groups.
- 2014, Christopher Hollings, Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups, page 249:
- Inverse semigroups are central to modern semigroup theory: arguably, they form the most-studied class of semigroups.
- 2002, Peter G. Trotter, A.9: Regular Semigroups, Aleksandr Vasilʹevich Mikhalev, Günter Pilz (editors), The Concise Handbook of Algebra, page 35,
Translations
semigroup in which every element has an inverse
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See also
- regular semigroup
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