Unpublished Notes of Ralph S. Freese
Since my papers often have saveral diagrams, PostScript is the easiest way
to get them. Some browsers may run ghostsview or xdvi on PostScript or dvi
files. If you want the file you may have to instruct your browser to
"save the next link as" a file. (On unix netscape, you can also press
the right mouse button on the link to get a menu.)
There is a new program called idvi which
allows you to
read tex papers over the net providing your browser has Java. It works
like xdvi. See my page on
Putting Mathematics on the Web for details and a comparison
with other methods.
If you have trouble getting any of these email me:
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 But this is superseded by my preprint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.