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→Regular *-semigroups (Nordahl & Scheiblich): MOS:MATH, MOS:PAREN. Added citation needed several places. Author + year is inadequate for finding the actual reference. D.B. McAlister published several results in 1968, I was unable to find one with the claim. |
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=== Regular *-semigroups (Nordahl & Scheiblich) ===
As mentioned in the [[#Examples|previous examples]], [[inverse semigroup]]s are a subclass of *-semigroups. It is also textbook knowledge that an inverse semigroup can be characterized as a regular semigroup in which any two idempotents commute. In 1963, [[Boris M. Schein]] showed that the following two axioms provide an analogous characterization of inverse semigroups as a [[Variety (universal algebra)|subvariety]] of *-semigroups:{{cn|date=
* {{math|''x'' {{=}} ''xx''*''x''}}
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