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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Semigroups with a dense subgroup

Author: W. S. Owen
Journal: Trans. Amer. Math. Soc. 212 (1975), 219-228
MSC: Primary 22A15
MathSciNet review: 0412330
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Abstract: The purpose of this paper is twofold. First, it is shown that the ideal structure of a semigroup with dense subgroup is closely related to its transformation group structure. That is, if a left orbit through a given point is locally compact, then the members of this orbit are precisely those elements which generate the same left ideal as the given point.

Secondly, the author gives a number of theorems which have as their goal the establishment of a natural product structure near a nonzero idempotent. Specifically the work of F. Knowles [11] is improved upon to include (1) the possibility of a nonconnected group; (2) the possibility of a nonsimply connected orbit; and (3) the case in which the boundary of the group is more than a single orbit.

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Keywords: Completely semisimple semigroup, dense Lie subgroup, Green's relations, local cross section, locally compact orbit
Article copyright: © Copyright 1975 American Mathematical Society