Advertisement

Siberian Mathematical Journal

, Volume 60, Issue 3, pp 526–541 | Cite as

Isomorphisms of Lattices of Subalgebras of Semifields of Positive Continuous Functions

  • V. V. SidorovEmail author
Article
  • 19 Downloads

Abstract

We consider the lattice of subalgebras of a semifield U(X) of positive continuous functions on an arbitrary topological space X and its sublattice of subalgebras with unity. We prove that each isomorphism of the lattices of subalgebras with unity of semifields U(X) and U(Y) is induced by a unique isomorphism of the semifields. The same result holds for lattices of all subalgebras excluding the case of the double-point Tychonoff extension of spaces.

Keywords

semifields of continuous functions subalgebra lattice of subalgebras isomorphism Hewitt space 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Sidorov V. V., “Definability of semifields of continuous positive functions by the lattices of their subalgebras,” Sb. Math., vol. 207, no. 9, 1267–1286 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Gillman L. and Jerison M., Rings of Continuous Functions, Springer-Verlag, New York (1976).zbMATHGoogle Scholar
  3. 3.
    Vechtomov E. M. and Sidorov V. V., “Isomorphisms of lattices of subalgebras of semirings of continuous nonnegative functions,” J. Math. Sci., vol. 177, no. 6, 817–846 (2011).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Sidorov V. V., “Lattices of subalgebras of semirings of continuous nonnegative functions with the max-plus,” J. Math. Sci., vol. 221, no. 3, 409–435 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Engelking R., General Topology, Heldermann Verlag, Berlin (1989).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Vyatka State UniversityKirovRussia

Personalised recommendations