Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T02:20:24.590Z Has data issue: false hasContentIssue false

L-semirings

Published online by Cambridge University Press:  09 April 2009

John Selden
Affiliation:
Clarkson College of TechnologyPotsdam, New York,
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.

By a topological semiring I mean a Hausdorff space together with two continuous associative operations, addition and multiplication, such that the multiplication distributes across the addition from both sides.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Mostert, P. S. and Shields, A. L., ‘On the structure of semigroups on a compact manifold with boundary’, Ann. of Math. 65 (1957), 117143.CrossRefGoogle Scholar
[2]Koch, R. J., ‘On monothetic semigroups’, Proc. Amer. Math. Soc. 8 (1957), 397401.CrossRefGoogle Scholar
[3]Selden, J., ‘A note on compact semirings’, Proc. Amer. Math. Soc. 15 (1964), 882886.CrossRefGoogle Scholar
[4]Selden, J., Theorems on topological semigroups and semirings (Dissertation, University of Georgia, 1963).Google Scholar
[5]Pearson, K. R., ‘Interval semirings on R1 with ordinary multiplication’, Jour. Australian Math. Soc. 6 (1966), 273288.CrossRefGoogle Scholar
[6]Pearson, K. R., ‘Certain topological semirings in R1’, Jour. Australian Math. Soc. 8 (1968), 171182.CrossRefGoogle Scholar