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The Word Problem for Orthogroups

Published online by Cambridge University Press:  20 November 2018

J. A. Gerhard and
Mario Petrich
J. A. Gerhard
Affiliation:
University of Manitoba, Winnipeg, Canada
Mario Petrich
Affiliation:
University of Manitoba, Winnipeg, Canada
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A semigroup which is a union of groups is said to be completely regular. If in addition the idempotents form a subsemigroup, the semigroup is said to be orthodox and is called an orthogroup. A completely regular semigroup S is provided in a natural way with a unary operation of inverse by letting a -l for a ∈ S be the group inverse of a in the maximal subgroup of S to which a belongs. This unary operation satisfies the identities

(1)

(2)

(3)

In fact a completely regular semigroup can be defined as a unary semigroup (a semigroup with an added unary operation) satisfying these identities. An orthogroup can be characterized as a completely regular semigroup satisfying the additional identity

(4)

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 4 , 01 August 1981, pp. 893 - 900
Copyright
Copyright © Canadian Mathematical Society 1981

References

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