The Word Problem for Orthogroups
1981 ◽
Vol 33
(4)
◽
pp. 893-900
◽
Keyword(s):
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)
1990 ◽
Vol 32
(2)
◽
pp. 137-152
◽
1977 ◽
Vol 29
(6)
◽
pp. 1171-1197
◽
2021 ◽
Vol 12
(3)
◽
pp. 5150-5155
1985 ◽
Vol 37
(2)
◽
pp. 271-295
◽
Keyword(s):