Skip to main content
SpringerLink
Log in

Homomorphisms of implicative semigroups

  • Research Article
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

Implicative semigroups and Brouwerian semigroups were studied by W. C. Nemitz and T. S. Blyth, respectively. In this paper, following the ideas of Nemitz and Blyth, we introduce the notion of negatively partially ordered implicative semigroups and studied the homomorphisms between these semigroups. Some results of Nemitz on implicative semilattices are generalized and amplified to implicative semigroups.

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. Birkhoff, G., “Lattice Theory,” Amer. Math. Soc. Colloquium. (1954).

  2. Blyth, T. S., “Pseudo-residuals in semigroups,” J. London Math. Soc.,40 (1965), 441–454.

    Article  MATH  MathSciNet  Google Scholar 

  3. Curry, H. B., “Foundations of Mathematics Logic,” McGraw-Hill, New York (1963).

    Google Scholar 

  4. Janowitz, M. F., and C. S. Johnson Jr.,A note on Brouwerian and Gilvenko semigroups, J. London Math. Soc.1 (1969), 733–736.

    Article  MATH  MathSciNet  Google Scholar 

  5. Nemitz, W. C.,Implicative semi-lattices, Trans. Amer. Math. Soc.,117 (1965), 128–142.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    M. W. Chan & K. P. Shum

Authors
  1. M. W. Chan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. P. Shum
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by L. N. Shevrin

Research is partially supported by CUHK small Project grant 220.600.080.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chan, M.W., Shum, K.P. Homomorphisms of implicative semigroups. Semigroup Forum 46, 7–15 (1993). https://doi.org/10.1007/BF02573537

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02573537

Keywords

Search

Navigation