Skip to main content
SpringerLink
Log in

A topology for complete semirings

  • Conference paper
  • First Online:
Book cover STACS 94 (STACS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 775))

Included in the following conference series:

  • 152 Accesses

Abstract

It is shown that every (algebraically) complete semiring has a “natural” topology associated with it. We discuss the relation between algebraic properties of the summation and separation axioms for the topology. This leads to a topological characterization of finitary semirings. The relation with the well-known Scott topology for complete partial orders (CPOs) is also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. H. Conway. Regular Algebra and Finite Machines. Chapman and Hall, 1971.

    Google Scholar 

  2. S. Eilenberg. Automata, Languages, and Machines, Vol. A. Academic Press, 1974.

    Google Scholar 

  3. M. Goldstern. Vervollständigung von Halbringen. Master's thesis, Technische Universität Wien, 1986.

    Google Scholar 

  4. C. A. Gunter and D. S. Scott. Semantic domains. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. B, Ch. 12, pp. 635–674. North-Holland, 1990.

    Google Scholar 

  5. U. Hebisch. Zur algebraischen Theorie unendlicher Summen in Halbgruppen und Halbringen. Habilitationsschrift, Technische Universität Clausthal-Zellerfeld, 1990.

    Google Scholar 

  6. G. Karner. On limits in complete semirings. Semigroup Forum, 45:148–165, 1992.

    Google Scholar 

  7. D. Krob. Monoides et semi-anneaux complets. Semigroup Forum, 36:323–339, 1987.

    Google Scholar 

  8. D. Krob. Monoides et semi-anneaux continus. Semigroup Forum, 37:59–78, 1987.

    Google Scholar 

  9. W. Kuich. Automata and languages generalized to Ω-continuous semirings. Theoretical Comput. Sci., 79:137–150, 1991.

    Google Scholar 

  10. W. Kuich and A. Salomaa. Semirings, Automata, Languages. Springer, 1986.

    Google Scholar 

  11. S. MacLane. Categories for the Working Mathematician. Springer, 1988.

    Google Scholar 

  12. G. Markovsky. Chain-complete posets and directed sets with applications. Algebra Universalis, 6:53–68, 1976.

    Google Scholar 

  13. H. J. Weinert. Generalized semialgebras over semirings. Lecture Notes in Mathematics, 1320:380–416, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Alcatel Austria Forschungszentrum, Ruthnergasse 1-7, A-1210, Wien, Austria

    Georg Karner

Authors
  1. Georg Karner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Patrice Enjalbert Ernst W. Mayr Klaus W. Wagner

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Karner, G. (1994). A topology for complete semirings. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_157

Download citation

  • DOI: https://doi.org/10.1007/3-540-57785-8_157

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57785-0

  • Online ISBN: 978-3-540-48332-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation