Unpublished Notes of Ralph S. Freese
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Partitions Algorithms. This is a 3 page note
describing efficient algorithms for calculations in partition
lattices. But this is superseded by my preprint
Computing congruences efficiently on my
Dean's Problem. This is an old lost problem in the theory of
free lattices. Only a partial solution is given.
Unique factorization under direct product.
In their book Algebras, Lattices, Varieties, the authors ask
for a common generalization of the Birkhoff-Ore and Jonsson Theorems.
They point out
that if the hypothesis of Lemma 4 on page 270 could be
weakened to Con A finite dimensional,
then general theorem would be true.
The first paper shows that if there is no homomorphism from the 4 elements
in question onto M_4, then the strengthened Lemma 4 is true.
The other paper
gives an example showing the desired strengthening of Lemma 4 is false. But
it is not a counter-example to the general result.
Moreover, there is a different conjectured extension of Lemma 4, which also
would imply the desired common generalization of the Birkhoff-Ore and
Jonsson theorems, that is still open. So this approach to the problem
is still viable.
Lectures on Projective Planes.
Some basics followed by a study of Hanna Neumann's embedding
of the Fano Plane into Hall Planes. This is motivated by the
question: are these subplanes maximal? If not what are the