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Solutions to some problems in amenable semigroups

Published online by Cambridge University Press:  14 November 2011

S. K. Ayyaswamy  and
P. V. Ramakrishnan
S. K. Ayyaswamy
Affiliation:
Arul Anandar College, Karuthmathur, Madurai-626 514, India
P. V. Ramakrishnan
Affiliation:
Department of Mathematics, Madurai Kamaraj University, Madurai-625 021, India
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Synopsis

This paper discusses a few problems on the size of the set of invariant means of an amenable semigroup posed by Maria M. Klawe, Alan L. T. Paterson and M. Rajagopalan and P. V. Ramakrishnan ([4], [5], [8] and [9]).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 104 , Issue 3-4 , 1986 , pp. 343 - 348
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

1Day, M. M.. Amenable Semigroups. Illinois J. Math. 1 (1957), 509–544.CrossRefGoogle Scholar
2Granirer, E.. A Theorem on Amenable semigroups. Trans. Amer. Maths. Soc. 111 (1964), 367–399.CrossRefGoogle Scholar
3Granirer, E.. Extremely Amenable Semigroups I and II. Math. Scand. 17 (1965a), 177–197; 20 (1967), 93–113.Google Scholar
4Klawe, Maria M.. On the dimension of left invariant means and left thick subsets. Trans. Amer. Math. Soc. 231 (1977), 507–518.CrossRefGoogle Scholar
5Maria, M. Klawe. Dimensions of the set of invariant means of semigroups, Illinois. J. Math. 24 (1980), 233–243.Google Scholar
6Mitchell, T.. Constant functions and left invariant means on semi-groups. Trans. Amer. Math. Soc. 119 (1965), 244–261.CrossRefGoogle Scholar
7Paterson, Alan L. T.. The size of the set of left invariant means on an ELA semigroup. Proc. Amer. Math. Soc. 72 (1978), 62–64.CrossRefGoogle Scholar
8Paterson, Alan L. T.. The cardinality of the set of left invariant means on a left amenable semigroup. Illinois. J. Math. 29 (1985) (to appear).Google Scholar
9Rajagopalan, M. and Ramakrishnan, P. V.. Uses of ßS in invariant means and extremely left amenable semigroups. Contemporary Mathematics, Amer. Math. 32.Google Scholar