Skip to main content
Log in

On left cancellative semigroups

  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

In this note we shall describe the structure of left cancellative semigroups. We shall also investigate the existence of idempotents and show that the existence of idempotents is related to the existence of maximal proper right ideals.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Burnell, D. G.,Left cancellative semigroups and an embedding problem, Doctoral Dissertation, University of California, Davis, 1970.

    Google Scholar 

  2. Clifford, A. H. and G. B. Preston,The algebraic theory of semigroups, Vol. I, Survey 7, Amer. Math. Soc., Providence, R.I., 1967.

    MATH  Google Scholar 

  3. —,The algebraic theory of semigroups, Vol. II, Amer. Math. Soc., Providence, R.I., 1967.

    MATH  Google Scholar 

  4. Dragunova, T. E.,The lattice of right ideals of left cancellative semigroups with identity, Usp. Mat. Nauk 12 (1957), 285–288 (in Russian).

    MathSciNet  Google Scholar 

  5. Petrich, M.,Introduction to semigroups, Vol. II (in preparation).

  6. Rees, D.,On the ideal structure of a semigroup satisfying a cancellation law, Quart. J. Math. Oxford (2) 19 (1948), 101–108.

    Article  MathSciNet  MATH  Google Scholar 

  7. Satyanarayana, M.,Semigroups admitting ring structure, Semigroup Forum (to appear).

  8. Schwarz, Š.On the structure of dual semigroups, Czechoslovak Math. J., 21 (96) 1971, 461–483.

    MathSciNet  MATH  Google Scholar 

  9. Šutov, E. G.,On some embedddings of cancellative semigroups, Mat. Sbornik 67 (1965), 167–180 (in Russian).

    Google Scholar 

  10. On semigroups with one-sided cancellation, Izv. Vysš. Učebn. Zav. Mat. 2(51) (1966), 137–147 (in Russian).

    MathSciNet  Google Scholar 

  11. Warne, R. J.,The direct product of right zero semigroups and certain groupoids, Amer. Math. Monthly 74 (1967), 160–164.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by Štefan Schwarz

Rights and permissions

Reprints and permissions

About this article

Cite this article

Satyanarayana, M. On left cancellative semigroups. Semigroup Forum 6, 317–329 (1973). https://doi.org/10.1007/BF02389139

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02389139

Keywords

Navigation