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An elegant 3-basis for inverse semigroups | | Joao Araujo
; Michael Kinyon
; | | Date: |
21 Mar 2010 | | Abstract: | It is well known that in every inverse semigroup the binary operation and the
unary operation of inversion satisfy the following three identities: [ quad
x=(xx’)x qquad quad (xx’)(y’y)=(y’y)(xx’) qquad quad (xy)z=x(yz’’),. ]
The goal of this note is to prove the converse, that is, we prove that every
unary semigroup satisfying these three identities is an inverse semigroup and
the unary operation coincides with the usual inversion on such semigroups. | | Source: | arXiv, 1003.4028 | | Services: | Forum | Review | PDF | Favorites | |
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