Skip to main content
SpringerLink
Log in

Bands of k-Archimedean semigroups

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

Abstract

In this paper we define the radical ϱ k (k∈Z +) of a relation ϱ on an arbitrary semigroup. Also, we define various types of k-regularity of semigroups and various types of k-Archimedness of semigroups. Using these notions we describe the structure of semigroups in which ρ k is a band (semilattice) congruence for some Green’s relation.

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. Bogdanović, S.: Semigroups of Galbiati-Veronesi. In: Proceedings of the Conference “Algebra and Logic”, Zagreb, 1984, pp. 9–20. University of Novi Sad, Novi Sad (1985)

    Google Scholar 

  2. Bogdanović, S.: Semigroups with a System of Subsemigroups. Institute of Mathematics, Novi Sad (1985)

    MATH  Google Scholar 

  3. Bogdanović, S., Ćirić, M.: Semigroups. Prosveta, Niš (1993), (in Serbian)

    MATH  Google Scholar 

  4. Bogdanović, S., Ćirić, M.: Semilattices of Archimedean semigroups and (completely) π-regular semigroups I (a survey). Filomat 7, 1–40 (1993)

    MATH  Google Scholar 

  5. Bogdanović, S., Ćirić, M.: A note on radicals of Green’s relations. Publ. Math. Debr. 47(3–4), 215–219 (1996)

    Google Scholar 

  6. Bogdanović, S., Ćirić, M.: Radicals of Green’s relations. Czechoslov. Math. J. 49(124), 683–688 (1999)

    Article  MATH  Google Scholar 

  7. Bogdanović, S., Ćirić, M., Novikov, B.: Bands of left Archimedean semigroups. Publ. Math. Debr. 52(1–2), 85–101 (1998)

    MATH  Google Scholar 

  8. Bogdanović, S., Ćirić, M., Popović, Ž.: Semilattice decompositions of semigroups revisited. Semigroup Forum 61, 263–276 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Bogdanović, S., Ćirić, M., Mitrović, M.: Semigroups satisfying certain regularity conditions. In: Shum, K.P., Wan, Z.X., Zhang, J.-P. (eds.) Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics in Hong Kong, 2002, pp. 46–59. World Scientific, Singapore (2003)

    Chapter  Google Scholar 

  10. Clifford, A.H.: Bands of semigroups. Proc. Am. Math. Soc. 5, 499–504 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  11. Harinath, K.S.: Some results on k-regular semigroups. Indian J. Pure Appl. Math. 10, 1422–1431 (1979)

    MATH  MathSciNet  Google Scholar 

  12. Higgins, P.M.: Techniques in Semigroup Theory. Oxford University Press, London (1992)

    Google Scholar 

  13. Howie, J.M.: An Introduction to Semigroup Theory. Academic Press, San Diego (1976)

    MATH  Google Scholar 

  14. Putcha, M.S.: Semigroups in which a power of each element lies in a subgroup. Semigroup Forum 5, 354–361 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  15. Putcha, M.S.: Semilattice decompositions of semigroups. Semigroup Forum 6, 12–34 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  16. Putcha, M.S.: Bands of t-Archimedean semigroups. Semigroup Forum 6, 232–239 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  17. Shevrin, L.N.: Theory of epigroups, I. Mat. Sb. 185(8), 129–160 (1994), (in Russian)

    MATH  Google Scholar 

  18. Tamura, T.: Nil-orders of commutative nil-bounded semigroups. Semigroup Forum 24, 255–262 (1982)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Economics, University of Niš, Trg Kralja Aleksandra 11, 18000, Niš, Serbia

    Stojan Bogdanović & Žarko Popović

  2. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, P.O. Box 224, 18000, Niš, Serbia

    Miroslav Ćirić

Authors
  1. Stojan Bogdanović
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Žarko Popović
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Miroslav Ćirić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Žarko Popović.

Additional information

Communicated by Boris M. Schein.

Research supported by Ministry of Science and Environmental Protection, Republic of Serbia, Grant No. 144011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bogdanović, S., Popović, Ž. & Ćirić, M. Bands of k-Archimedean semigroups. Semigroup Forum 80, 426–439 (2010). https://doi.org/10.1007/s00233-010-9208-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-010-9208-3

Keywords

Search

Navigation