Advertisement

algebra universalis

, Volume 41, Issue 2, pp 151–153 | Cite as

Sublattices and standard congruences

  • G. Grätzer
  • E. T. Schmidt

Abstract.

In an earlier paper, the authors and H. Lakser proved that, for every lattice K and nontrivial congruence \( \phi \) of K, there is an extension L of K such that \( \phi \) is the restriction to K of a standard congruence on L. ¶In this note, we give a very short proof of this result in a stronger form the lattice L we construct is sectionally complemented and it has only one nontrivial congruence, the standard congruence.

Key words and phrases: Congruence lattice, congruence-preserving embedding, sectionally comple mented, standard. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag Basel, 1999

Authors and Affiliations

  • G. Grätzer
    • 1
  • E. T. Schmidt
    • 2
  1. 1.Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada, e-mail: gratzer@cc.umanitoba.ca, URL http//www.maths.umanitoba.ca/homepages/gratzer.html/ CA
  2. 2.Mathematical Institute of the Technical University of Budapest, Müegyetem Rkp. 3, H-1521 Budapest, Hungary, e-mail: schmidt@math.bme.hu, URL http//www.math.bme.hu/˜schmidt/HU

Personalised recommendations