Skip to main content
SpringerLink
Log in

Right Cones in Groups

  • Conference paper
Advances in Ring Theory

Part of the book series: Trends in Mathematics ((TM))

  • 332 Accesses

Abstract

A right cone C in a group G is a submonoid of G that generates G and aC ⊆ bC or bC ⊂ aC holds for any a, b in C; such a right cone is closely related to the cones of (right) linearly ordered groups on the one hand and valuation rings, in particular right chain domains, on the other. The ideal theory of right cones is described, the rank one right cones are classified, and three problems are raised.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brungs, H.H., Dubrovin, N.I., Classification of chain rings, preprint.

    Google Scholar 

  2. Brungs, H.H., Schröder, M., Prime segments of skew fields, Can. J. Math. 47 (1995), 1148–1176.

    Article  MATH  Google Scholar 

  3. Brungs, H.H.,Törner, G., Right chain domains with prescribed value holoids, J. Algebra 176 (1995), 346–355.

    Article  MathSciNet  MATH  Google Scholar 

  4. Cohn, P.M., Free Ideal Rings and Their Relations, Academic Press, London, 1985.

    Google Scholar 

  5. Dubrovin, N.I., The rational closure of group rings of left orderable groups, Schriftenreihe des Fachbereichs Mathematik, Vol. 254, Universität Duisburg, 96pp, 1994.

    Google Scholar 

  6. Fuchs, L., Teilweise geordnete algebraische Strukturen, Vandenhoeck and Ruprecht, Göttingen, 1966.

    MATH  Google Scholar 

  7. Jategaonkar, A.V., A counter-example in ring theory and homological algebra, J. Algebra 12 (1969), 418–440.

    Article  MathSciNet  MATH  Google Scholar 

  8. Smirnov, D.M., Right-ordered groups, Algebra i Logika 5:6 (1966), 41–59.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, Т6G 2G1

    H. H. Brungs

  2. Fachbereich Mathematik, Gerhard-Mercator-Universität, 47048, Duisburg, Germany

    G. Törner

Authors
  1. H. H. Brungs
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Törner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Ohio University, Athens, OH, 45701, USA

    S. K. Jain

  2. Department of Mathematics, Ohio State University at Lima, Lima, OH, 45804, USA

    S. Tariq Rizvi

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this paper

Cite this paper

Brungs, H.H., Törner, G. (1997). Right Cones in Groups. In: Jain, S.K., Rizvi, S.T. (eds) Advances in Ring Theory. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1978-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-1978-1_6

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7364-6

  • Online ISBN: 978-1-4612-1978-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation