Skip to main content
SpringerLink
Log in

On congruence extension properties for ordered algebras

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We introduce four extension properties (CEP, QEP, SCEP and SQEP) for ordered algebras, similar to the congruence extension property (CEP) and the strong congruence extension property of usual (unordered) algebras. All four properties turn out to have a description in terms of commutative squares or pullback diagrams. We then use these categorical descriptions to prove an ordered analogue of the well-known relation TP = AP + CEP, namely that a variety of ordered algebras has the ordered transferability property if and only if it has the ordered amalgamation property and QEP.

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

References

  1. S.L. Bloom, Varieties of ordered algebras. J. Comput. Syst. Sci. 13, 200–212 (1976)

    Article  Google Scholar 

  2. S. Bulman-Fleming, N. Sohail, Examples concerning absolute flatness and amalgamation in pomonoids. Semigroup Forum 80, 272–292 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. G. Czédli, A. Lenkehegyi, On congruence \(n\)-distributivity of ordered algebras, Acta Math. Hung. 41, 17–26 (1983)

    Article  MATH  Google Scholar 

  4. G. Czédli, A. Lenkehegyi, On classes of ordered algebras and quasiorder distributivity, Acta Sci. Math. 46, 41–54 (1983)

    MATH  Google Scholar 

  5. J.I. Garcia, The congruence extension propery for algebraic semigroups. Semigroup Forum 43, 1–18 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  6. V. Gould, M. Wild, Every Hamiltonian variety has the congruence extension property—a short proof. Algebra Univers 26, 187–188 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  7. E.W. Kiss, L. Márki, P. Pröhle, W. Tholen, Categorical algebraic properties. A compendium on amalgamation, congruence extension, epimorphisms, residual smallness, and injectivity. Stud. Sci. Math. Hung. 18, 79–141 (1983)

    MATH  Google Scholar 

  8. V. Laan, N. Sohail, On mono- and epimorphisms in varieties of ordered algebras, to appear

Download references

Acknowledgments

We are very grateful to Professor George Janelidze for pointing out the idea behind Theorem 4.2. We also wish to thank the referee for useful suggestions. This research was supported by Estonian Institutional Research Project IUT20-57. The second named author is a recepient of the Estonian Science Foundation’s MOBILITAS research grant MJD 198.

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Institute of Mathematics, University of Tartu, J. Liivi 2, Tartu, 50409, Estonia

    Valdis Laan & Lauri Tart

  2. Department of Mathematics, Physics and Geology Cape Breton University, 1250 Grand Lake Rd., Sydney, NS, B1P 6L2, Canada

    Sohail Nasir

Authors
  1. Valdis Laan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sohail Nasir
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lauri Tart
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valdis Laan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Laan, V., Nasir, S. & Tart, L. On congruence extension properties for ordered algebras. Period Math Hung 71, 92–111 (2015). https://doi.org/10.1007/s10998-015-0088-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-015-0088-x

Keywords

Mathematics Subject Classification

Search

Navigation