Skip to main content
SpringerLink
Log in

A property of transformation semigroups

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

Abstract

A semigroup S (with zero) is called right resp. left (0-) quasiresiduated with respect to its natural partial order ≤ S if for any a,b∈S (a,b≠0) there exists x∈S (x≠0) resp. y∈S (y≠0) such that ax≤ S b resp. ya≤ S b. It is shown that the most important semigroups of mappings are—at least for finite sets and finite-dimensional vector spaces—left and/or right (0-) quasiresiduated.

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. Blyth, T.S.: Residuated inverse semigroups. J. Lond. Math. Soc. 1, 243–248 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blyth, T.S., Janowitz, M.F.: Residuation Theory. Pergamon Press, Oxford (1972)

    MATH  Google Scholar 

  3. Howie, J.M.: An Introduction to Semigroup Theory. Academic Press, London (1976)

    MATH  Google Scholar 

  4. Fuchs, L.: Partially Ordered Algebraic Systems. Pergamon Press, Oxford (1963)

    MATH  Google Scholar 

  5. Kowol, G., Mitsch, H.: Naturally ordered transformation semigroups. Mon. Math. 102, 115–138 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  6. Mitsch, H.: A natural partial order for semigroups. Proc. Am. Math. Soc. 97, 384–388 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mitsch, H.: Quasiresiduals in semigroups with natural partial order (submitted)

Download references

Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Wien, 1090, Wien, Nordbergstr. 15, Austria

    H. Mitsch

Authors
  1. H. Mitsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Mitsch.

Additional information

Communicated by Mark V. Lawson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mitsch, H. A property of transformation semigroups. Semigroup Forum 85, 91–96 (2012). https://doi.org/10.1007/s00233-012-9381-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-012-9381-7

Keywords

Search

Navigation