Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T14:07:25.756Z Has data issue: false hasContentIssue false
  • English
  • Français

L-semirings

Published online by Cambridge University Press:  09 April 2009

John Selden
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
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 4 , June 1972 , pp. 391 - 394
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), 117–143.CrossRefGoogle Scholar
[2]Koch, R. J., ‘On monothetic semigroups’, Proc. Amer. Math. Soc. 8 (1957), 397–401.CrossRefGoogle Scholar
[3]Selden, J., ‘A note on compact semirings’, Proc. Amer. Math. Soc. 15 (1964), 882–886.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), 273–288.CrossRefGoogle Scholar
[6]Pearson, K. R., ‘Certain topological semirings in R1’, Jour. Australian Math. Soc. 8 (1968), 171–182.CrossRefGoogle Scholar