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Primitive idempotent measures on compact semitopological semigroups

Published online by Cambridge University Press:  09 April 2009

Stephen T. L. Choy
Stephen T. L. Choy
Affiliation:
University of Hong Kong and University of Singapore
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For a semigroup S let I(S) be the set of idempotents in S. A natural partial order of I(S) is defined by e ≦ f if ef = fe = e. An element e in I(S) is called a primitive idempotent if e is a minimal non-zero element of the partially ordered set (I(S), ≦). It is easy to see that an idempotent e in S is primitive if and only if, for any idempotent f in S, f = ef = fe implies f = e or f is the zero element of S. One may also easily verify that an idempotent e is primitive if and only if the only idempotents in eSe are e and the zero element. We let П(S) denote the set of primitive idempotent in S.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 4 , June 1972 , pp. 451 - 455
Copyright
Copyright © Australian Mathematical Society 1972

References

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