Skip to main content
SpringerLink
Log in

The axiomatizability of the class of root closed monoids

  • SHORT NOTE
  • Published:
Semigroup Forum Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We prove that the theory of root closed monoids is axiomatizable, but not finitely axiomatizable. Some directions for further research are presented.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. in the language \(\mathbf {L}\) consisting of equality, a binary function symbol \(\mathbf {\cdot }\), and a constant symbol \(\mathbf {1}\).

  2. \(Cn(\sum _0)\) is the set of all sentences logically implied by \(\sum _0\).

References

  1. Gilmer, R.: Commutative Semigroup Rings. The University of Chicago Press, Chicago (1984)

    MATH  Google Scholar 

  2. Gilmer, R.: Multiplicative ideal theory. Corrected reprint of the 1972 edition. Queen’s Papers in Pure and Applied Mathematics, 90. Queen’s University, Kingston (1992)

Download references

Acknowledgments

The authors warmly thank the anonymous referee for providing several comments which improved the manuscript as well as for suggesting Problem 2 above.

Author information

Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, Newark, OH, 43055, USA

    K. Alan Loper & Nicholas J. Werner

  2. Department of Mathematics, The University of Colorado, Colorado Springs, CO, 80918, USA

    Greg Oman

Authors
  1. K. Alan Loper
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Greg Oman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicholas J. Werner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Greg Oman.

Additional information

Communicated by Victoria Gould.

All monoids in this paper are assumed cancellative and commutative.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alan Loper, K., Oman, G. & Werner, N.J. The axiomatizability of the class of root closed monoids. Semigroup Forum 91, 737–740 (2015). https://doi.org/10.1007/s00233-014-9675-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-014-9675-z

Keywords

Search

Navigation