Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-28T16:05:04.226Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Beidleman-Cox, , ‘Topological near-rings’, Archive der Mathematik, 18 (1967), 485–492.Google Scholar
[2]Day, Jane M., ‘Expository Lectures on Topological Semigroups”, in Arbib, M. A. (editor), Machines, Languages and Semigroups (Academic Press, New York, 1968).Google Scholar
[3]Hofmann-Mostert, , Elements of Compact Semigroups (Merrill, 1966).Google Scholar
[4]Kaplansky, Irving, ‘Topological rings’, Amer. Journal Math. (19) 153–183.Google Scholar
[5]Montgomary, D. and Zippin, , Topological transformation groups, (Interscience, New York, 1955).Google Scholar
[6]Mycielski, Jan, ‘Some properties of connected compact groups’, Colloquium Mathematicum 5 (1958), 162–166.Google Scholar
[7]Paalman-de Miranda, A. B., Topological Semigroups (Mathematisch Zentrum, Amsterdam, 1964).Google Scholar
[8]Pearson, K. R., The three kernels of a compact semiring, Journal Aus. Math. Soc. 10 (1969), 299–319.Google Scholar
[9]Selden, John, ‘A note on compact semirings’, Proc. Amer. Math. Soc. 15 (1964), 882–886.Google Scholar