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inverse semigroup

inverse semigroup noun: a semigroup in which every element x has an inverse y, such that x = xyx and y = yxy.

Noun

inverse semigroup (plural inverse semigroups)

  1. A semigroup in which every element x has an inverse y, such that x = xyx and y = yxy.
    • 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.2002, Peter G. Trotter, “A.9: Regular Semigroups”, in Aleksandr Vasilʹevich Mikhalev, Günter Pilz, editors, The Concise Handbook of Algebra, page 35
    • Inverse semigroups form a class of semigroups which are closest (in some sense) to groups.2008, Olexandr Ganyushkin, Volodymyr Mazorchuk, Classical Finite Transformation Semigroups: An Introduction, page v

Forms of inverse semigroup

pluralinverse semigroups

Questions about inverse semigroup

What does inverse semigroup mean?
Inverse semigroup means a semigroup in which every element x has an inverse y, such that x = xyx and y = yxy.
What part of speech is inverse semigroup?
Inverse semigroup is a noun.
What is the plural of inverse semigroup?
The plural of inverse semigroup is inverse semigroups.

Words near inverse semigroup in the dictionary

  1. inverse matrix
  2. inverse matrixes
  3. inverse number
  4. inverse proportion
  5. inverse Pythagorean theorem
  6. inverse semigroup
  7. inverse semigroups
  8. inverse sine
  9. inverse sines
  10. inverse spelling
  11. inverse spellings

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Adapted from Wiktionary: inverse semigroup (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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