See inverse semigroup on Wiktionary
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"ref": "2002, Peter G. Trotter, “A.9: Regular Semigroups”, in Aleksandr Vasilʹevich Mikhalev, Günter Pilz, editors, The Concise Handbook of Algebra, page 35:",
"text": "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.",
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"ref": "2008, Olexandr Ganyushkin, Volodymyr Mazorchuk, Classical Finite Transformation Semigroups: An Introduction, page v:",
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"A semigroup in which every element x has an inverse y, such that x = xyx and y = yxy."
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