Semigroup with involution: Difference between revisions

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The semigroup ''S'' with the involution * is called a semigroup with involution.

In some applications, the second of these axioms has been called [[antidistributive]].<ref name="BrinkKahl1997">{{cite book|author1=Chris Brink|author2=Wolfram Kahl|author3=Gunther Schmidt|title=Relational Methods in Computer Science|date=1997|publisher=Springer|isbn=978-3-211-82971-4|page=4}}</ref> Semigroups that satisfy only the first of these axioms belong to the larger class of [[U-semigroup]]s.

In some applications, the second of these axioms has been called [[antidistributive]].<ref name="BrinkKahl1997">{{cite book|author1=Chris Brink|author2=Wolfram Kahl|author3=Gunther Schmidt|title=Relational Methods in Computer Science|date=1997|publisher=Springer|isbn=978-3-211-82971-4|page=4}}</ref> Regarding the natural philosophy of this axiom, [[Harold Scott MacDonald Coxeter|H.S.M. Coxeter]] remarked that it "becomes clear when we think of [x] and [y] as the operations of putting on our socks and shoes, respectively."<ref>H.S.M. Coxeter, ''Introduction to Geometry'', p. 33</ref>

==Examples==