Skip to main content
SpringerLink
Log in

Structure of a finite commutative inverse semigroup and a finite bundle for which the inverse monoid of local automorphisms is permutable

  • Published:
Ukrainian Mathematical Journal Aims and scope

For a semigroup S, the set of all isomorphisms between the subsemigroups of the semigroup S with respect to composition is an inverse monoid denoted by PA(S) and called the monoid of local automorphisms of the semigroup S. The semigroup S is called permutable if, for any couple of congruences ρ and σ on S, we have ρ ∘ σ = σ ∘ ρ. We describe the structures of a finite commutative inverse semigroup and a finite bundle whose monoids of local automorphisms are permutable.

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. A. L. Libikh, “Inverse semigroups of the local automorphisms of Abelian groups,” in: Investigations in Algebra [in Russian], Issue 3 (1973), pp. 25–33.

  2. S. M. Goberstein, “Inverse semigroups with certain types of partial automorphism monoids,” Glasgow Math. J., 32, 189–195 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  3. V. D. Derech, “Characterization of the semilattice of idempotents of a finite-rank permutable inverse semigroup with zero,” Ukr. Mat. Zh., 59, No. 10, 1353–1362 (2007); English translation: Ukr. Math. J., 59, No. 10, 1517–1527 (2007).

    Article  MathSciNet  Google Scholar 

  4. V. D. Derech, “Congruences of a permutable inverse semigroup of finite rank,” Ukr. Mat. Zh., 57, No. 4, 469–473 (2005); English translation: Ukr. Math. J., 57, No. 4, 565–570 (2005).

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Hall, Jr., The Theory of Groups, Macmillan Company, New York (1959).

    MATH  Google Scholar 

  8. O. Ganyushkin and V. Mazorchuk, Classical Finite Transformation Semigroups. An Introduction, Springer, London (2009).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vinnytsya National Technical University, Vinnytsya, Ukraine

    V. D. Derech

Authors
  1. V. D. Derech
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 9, pp. 1218–1226, September, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Derech, V.D. Structure of a finite commutative inverse semigroup and a finite bundle for which the inverse monoid of local automorphisms is permutable. Ukr Math J 63, 1390–1399 (2012). https://doi.org/10.1007/s11253-012-0586-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-012-0586-4

Keywords

Search

Navigation