Skip to main content
Log in

Structure of a finite inverse semigroup with zero every stable order on which is fundamental or antifundamental

  • Published:
Ukrainian Mathematical Journal Aims and scope

We establish necessary and sufficient conditions for any stable order on a finite inverse semigroup with zero to be fundamental or antifundamental.

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. V. V. Vagner, “Representation of ordered semigroups,” Mat. Sb., 38, No. 2, 203–240 (1956).

    MathSciNet  Google Scholar 

  2. B. M. Shain, “Representation of ordered semigroups,” Mat. Sb., 65, No. 2, 188–197 (1964).

    MathSciNet  Google Scholar 

  3. S. M. Goberstein, “Fundamental order relations on inverse semigroups and on their generalizations,” Semigroup Forum, 21, 285–328 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  4. M. G. Mogilevskii, “Order relations on symmetric semigroups of transformations and on their homomorphic images,” Semigroup Forum, 19, 283–305 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  5. M. G. Mogilevskii, “Order relations on a symmetric inverse semigroup,” Teor. Polugrup. Prilozh., Issue 3, 63–70 (1974).

    Google Scholar 

  6. M. V. Beilis, “Stable order relations on a semigroup of partial transformations of bounded rank,” Teor. Polugrup. Prilozh., Issue 5, 3–9 (1985).

    Google Scholar 

  7. V. D. Derech, “Maximum stable orders on inverse semigroups of finite rank with zero,” Ukr. Mat. Zh., 60, No. 8, 1035–1041 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  8. V. D. Derech, “Structure of the Munn semigroup of finite rank each stable order of which is either fundamental or antifundamental,” Ukr. Mat. Zh., 61, No. 1, 52–60 (2009).

    Article  MathSciNet  Google Scholar 

  9. V. D. Derech, “Congruences of a permutable inverse semigroup of finite rank,” Ukr. Mat. Zh., 57, No. 4, 469–473 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  10. A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vols. 1, 2, American Mathematical Society, Providence, RI (1964, 1967).

    Google Scholar 

  11. M. Petrich, Inverse Semigroups, Wiley, New York (1984).

    MATH  Google Scholar 

  12. A. G. Kurosh, Lectures in General Algebra [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  13. H. Hamilton, “Permutability of congruences on commutative semigroups,” Semigroup Forum, 10, 55–66 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  14. V. D. Derech, “Characteristics of the semilattice of idempotents of a permutable inverse semigroup of finite rank with zero,” Ukr. Mat. Zh., 59, No. 10, 1353–1362 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  15. B. M. Schein, “Completions, translational hulls, and ideal extensions of inverse semigroups,” Czech. Math. J., 23, 575–610 (1973).

    MathSciNet  Google Scholar 

  16. V. D. Derech, “Maximum stable orders on some biideal extensions of the Brand semigroup,” in: Semigroups and Their Homomorphisms [in Russian], Leningrad (1991), pp. 12–18.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 1, pp. 29–39, January, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Derech, V.D. Structure of a finite inverse semigroup with zero every stable order on which is fundamental or antifundamental. Ukr Math J 62, 31–42 (2010). https://doi.org/10.1007/s11253-010-0331-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-010-0331-9

Keywords

Navigation