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Product structure in topological algebras

Published online by Cambridge University Press:  09 April 2009

Desmond A. Robbie
Desmond A. Robbie
Affiliation:
Department of Mathematics, Adelaide College of Advanced EducationAdelaide, South Australia.
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It is shown that every compact nonconnected semigroup (semiring) which has commuting congruences, has a nontrivial continous homomorphic image which is iseomorphic to a direct product of finite congruence free semigroups (semirings). (This extends parts of earlier work by Kaplansky (1947) on compact rings.) It is also shown that there is a possibly finer representation but onto a product of congruence free semigroups (semirings) known only to be compact Hausdorff. A number of the techniques used evolve from work of Professor Wallace, who retired in mid-1973, and to whom this paper is dedicated.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 4 , November 1975 , pp. 385 - 393
Copyright
Copyright © Australian Mathematical Society 1975

References

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