Next Meeting

Topics:

Cancellation and distributivity in skew lattices Michael Kinyon Denver University In lattices, distributivity and cancellation are equivalent notions, and they are characterized by the nonoccurrence of certain forbidden sublattices. Skew lattices are a noncommutative generalization of lattices. For instance, skew lattices of idempotents occur in certain rings. In skew lattices, cancellation and distributivity are not equivalent. In this talk, I will discuss recent success in characterizing cancellation in terms of the nonoccurrence of forbidden subalgebras. As a byproduct, the class of cancellative skew lattices forms a variety. If time permits, I will describe progress toward a forbidden subalgebra characterization of distributivity.

Inherited Ovals in finite Moulton Planes W. E. Cherowitzo U C D Finding ovals (or proving that they don't exist) in non-Desarguesian planes that are not amenable to computer searches is a daunting problem. Many of the known examples are inherited from the Desarguesian plane of the same order in the sense that if one views the non-Desarguesian plane as the point set of the Desarguesian plane on which one redefines the lines, an oval remains an oval under the new line definition. In this talk we will look at a purported proof that finite Moulton planes of even order can not contain inherited ovals that lie in a hyperconic of the corresponding Desarguesian plane.