On the dimension of left invariant means and left thick subsets
Author:
Maria Klawe
Journal:
Trans. Amer. Math. Soc. 231 (1977), 507518
MSC:
Primary 43A07
MathSciNet review:
0447970
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Abstract: If S is a left amenable semigroup, let denote the dimension of the set of left invariant means on S. Theorem. If S is left amenable, then if and only if S contains exactly n disjoint finite left ideal groups. This result was proved by Granirer for S countable or left cancellative. Moreover, when S is infinite, left amenable, and either left or right cancellative, we show that is at least the cardinality of S. An application of these results shows that the radical of the second conjugate algebra of is infinite dimensional when S is a left amenable semigroup which does not contain a finite ideal.
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 Theodore Mitchell, Constant functions and left invariant means on semigroups, Trans. Amer. Math. Soc. 119 (1965), 244261. MR 33 #1743. MR 0193523 (33:1743)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197704479705
PII:
S 00029947(1977)04479705
Keywords:
Semigroup,
left thick,
invariant means,
radical,
finite left ideal group
Article copyright:
© Copyright 1977
American Mathematical Society
