Unpublished Notes of Ralph S. Freese

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1. 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 But this is superseded by my preprint Computing congruences efficiently on my papers page.

2. Dean's Problem. This is an old lost problem in the theory of free lattices. Only a partial solution is given.

3. 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.

4. 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 intermediate planes?