Embedding topological semigroups in topological groups
1970 ◽
Vol 17
(2)
◽
pp. 127-138
◽
Keyword(s):
If we consider a semigroup, its algebraic structure may be such that it is isomorphic to a subsemigroup of a group, or is algebraically embeddable in a group. This problem was investigated in 1931 by Ore who obtained in (4) a set of necessary conditions for this embedding. A necessary condition is that the semigroup should be cancellative: for any a, x, y in the semigroup either xa = ya or ax = ay implies that x = y. Malcev in (3) showed that this was not sufficient. It is enough to note that his example was a non-commutative semigroup: a commutative cancellative semigroup is embeddable algebraically in a group.
Keyword(s):
1977 ◽
Vol 23
(1)
◽
pp. 46-58
◽
Keyword(s):
2001 ◽
Vol 27
(6)
◽
pp. 387-389
◽
Keyword(s):
1954 ◽
Vol 6
◽
pp. 186-189
◽
1986 ◽
Vol 13
(1)
◽
pp. 46-52
◽
1998 ◽
Vol 06
(01)
◽
pp. 3-9
◽