Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-24T14:11:21.691Z Has data issue: false hasContentIssue false
  • English
  • Français

Double ideals in compact semirings

Published online by Cambridge University Press:  09 April 2009

Martha Bertman  and
John Selden
Martha Bertman
Affiliation:
Department of Mathematics Clarkson College of Technology Potsdam, New York
John Selden
Affiliation:
Department of Mathematics Clarkson College of Technology Potsdam, 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 we mean a Hausdorff space S together with two continuous associative operations on S such that one (called multiplication) distributes across the other (called addition). That is, we insist that for all x, y and z in S. Note that, in contrast to the purely algebraic situation [1,2], we do not postulate the existence of an additive identity which is a multiplicative zero.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 1 , February 1973 , pp. 123 - 128
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Bourne, S., ‘The Jacobson radical of a semiring,’ Proc. Nat. Acad. Sci. U. S. A. 37 (1951), 163–170.CrossRefGoogle ScholarPubMed
[2]Bourne, S., ‘On multiplicative idempotents of a potent semiring,’ Proc. Nat. Acad. Sci. U. S. A. 42 (1956), 632–638.CrossRefGoogle ScholarPubMed
[3]Bourne, S., ‘On compact semirings’, Proc. Jap. Acad., 35 (1959), 332–334.Google Scholar
[4]Wallace, A. D., ‘The structure of topological semigroups,’, Bull. Amer. Math. Soc. 61 (1955), 95–112.CrossRefGoogle Scholar
[5]Hofmann, K. H. and Mostert, P. S., Elements of Compact Semigroups (Columbus, Ohio 1966).Google Scholar
[6]DeMiranda, A. B. Paalman, Topological Semigroups (Mathematisch Centrum, Amsterdam 1964), 45.Google Scholar