Skip to main content
SpringerLink
Log in

Isotone mapping of free lattices

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

An arbitrary partially ordered set P and an isotone mappingϕ of this set into a complete lattice L are considered. It is proved that the mappingϕ can be extended to an isotone mappingϕ of the lattice FL(P) into the lattice L.

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

Literature cited

  1. R. P. Dilworth, “Lattices with unique complements,” Trans. Amer. Math. Soc.,57, 123–154 (1945).

    Google Scholar 

  2. R. A. Dean, “Free lattices generated by partially ordered sets and preserving bounds,” Canad. J. Math.,16, No. 1, 136–148 (1964).

    Google Scholar 

  3. Yu. I. Sorkin, “Free unions of lattices,” Matem. Sb.,30, 677–694 (1952).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Institute of Chemical Engineering, USSR

    T. S. Fofanova

Authors
  1. T. S. Fofanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 405–416, October, 1968.

The author is deeply indebted to L. A. Skornyakov, under whose guidance the work has been done.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fofanova, T.S. Isotone mapping of free lattices. Mathematical Notes of the Academy of Sciences of the USSR 4, 734–741 (1968). https://doi.org/10.1007/BF01093711

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01093711

Keywords

Search

Navigation