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Dispersal in compact semimodules

Published online by Cambridge University Press:  09 April 2009

Alexander Doniphan Wallace
Alexander Doniphan Wallace
Affiliation:
The University of Florida, Gainesville, Florida, U.S.A.
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A semigroup is a nonvoid Hausdorff space together with a continuous associative operation. A semiring is a nonvoid Hausdorff space together with a couple of continuous associative operations, one of which (usually denoted as multiplication) distributes over the other (usually denoted as addition). If R is a semiring then an R-semimodule is a semigroup M under addition together with a continuous operation R × M → M which satisfies the associativity and distributivity conditions usually stipulated in the instance of an R-module. It is purpose of this paper to establish for semimodules certain propositions proved by Kaplansky [4], Pearson [8], Selden [9], Beidleman-Cox [1] and others.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 3 , May 1972 , pp. 338 - 342
Copyright
Copyright © Australian Mathematical Society 1972

References

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