Abstract
I shall discuss a very simple, frustrating, tantalizing question in ring theory, some partial results I have obtained on it, and some possible methods of further attack, which the reader is invited to pursue. The problem comes from the theory of division algebras, but the approach to be described will lead us through general ring theory, linear algebra, algebraic geometry and category theory. (We shall make a detour into semigroup theory as well.) Which fields may hold the methods by which the problem can be solved I do not know; but I think this paper contains ideas which should be of interest to people in all the areas mentioned.
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