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Congruence-preserving extensions of finite lattices to sectionally complemented lattices
Author(s):
G.
Grätzer;
E.
T.
Schmidt
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1903-1915.
MSC (1991):
Primary 06B10;
Secondary 08A05
Posted:
March 3, 1999
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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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- 2.
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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, Muegyetem rkp.~3, H-1521 Budapest, Hungary
Email:
schmidt@math.bme.hu
DOI:
10.1090/S0002-9939-99-04671-7
PII:
S 0002-9939(99)04671-7
Keywords:
Congruence lattice,
congruence-preserving embedding,
sectionally complemented lattice,
finite
Received by editor(s):
July 16, 1996
Received by editor(s) in revised form:
September 22, 1997
Posted:
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 of article:
Copyright
1999,
American Mathematical Society
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