View source for Involution semigroup

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A [[semigroup]] $(S,{\cdot})$ with an involution $*$, having the properties $(x\cdot y)^* = y^* \cdot x^*$ and $x^{{*}{*}} = x$.

A ''projection'' in an involution semigroup is an element $e$ such that $e\cdot e = e = e^*$.  There is a partial order on projections given by $e \le f$ if $e\cdot f = e$.  

A ''regular involution'' semigroup is one in which $x x^* x = x$: that is, it is also a [[regular semi-group|regular semigroup]] in which the involution acts as generalised inverse.

====References====
* Ivan Rival (ed.),"Algorithms and Order", Kluwer (1989) {{ISBN|940107691X}} {{ZBL|0709.68004}}