Congruence-preserving extensions of finite lattices to sectionally complemented lattices
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- by G. Grätzer and E. T. Schmidt PDF
- Proc. Amer. Math. Soc. 127 (1999), 1903-1915 Request permission
Abstract:
In 1962, the authors proved that every finite distributive lattice can be represented as the congruence lattice of a finite sectionally complemented lattice. In 1992, M. Tischendorf verified that every finite lattice has a congruence-preserving extension to an atomistic lattice. In this paper, we bring these two results together. We prove that every finite lattice has a congruence-preserving extension to a finite sectionally complemented lattice.References
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Additional Information
- G. Grätzer
- Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
- Email: gratzer@cc.umanitoba.ca
- E. T. Schmidt
- Affiliation: Mathematical Institute of the Technical University of Budapest, Műegyetem rkp. 3, H-1521 Budapest, Hungary
- Email: schmidt@math.bme.hu
- Received by editor(s): July 16, 1996
- Received by editor(s) in revised form: September 22, 1997
- Published electronically: March 3, 1999
- Additional Notes: The research of the first author was supported by the NSERC of Canada.
The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. T7442. - Communicated by: Lance W. Small
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1903-1915
- MSC (1991): Primary 06B10; Secondary 08A05
- DOI: https://doi.org/10.1090/S0002-9939-99-04671-7
- MathSciNet review: 1476133