Abstract. J. Tůma proved an interesting ``congruence amalgamation'' result. We are generalizing and providing an alternate proof for it. We then provide applications of this result: \item{(i)} A. P. Huhn proved that every distributive algebraic lattice $D$ with at most $\aleph_1$ compact elements can be represented as the congruence lattice of a lattice $L$. We show that $L$ can be constructed as a locally finite relatively complemented lattice with zero. \item{(ii)} We find a large class of lattices, the {\it $\omega $-congruence-finite} lattices, that contains all locally finite countable lattices, in which every lattice has a relatively complemented congruence-preserving extension.
AMS Subject Classification
(1991): 06B05, 06B10, 06D05
Keyword(s):
Congruence,
amalgamation,
lattice,
distributive,
relative complemented
Received March 10, 1999. (Registered under 2717/2009.)
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