Involution semigroup
From Encyclopedia of Mathematics
Revision as of 19:32, 17 January 2021 by Richard Pinch (talk | contribs) (Start article: Involution semigroup)
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
2020 Mathematics Subject Classification: Primary: 20M10 [MSN][ZBL]
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 semigroup in which the involution acts as generalised inverse.
References
- Ivan Rival (ed.),"Algorithms and Order", Kluwer (1989) ISBN 940107691X Zbl 0709.68004
How to Cite This Entry:
Involution semigroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Involution_semigroup&oldid=51369
Involution semigroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Involution_semigroup&oldid=51369