7 April 2009
2:30 - 4:00   M Barr
A duality for certain module categories
Joint with J. Kennison and R. Raphael

Abstract: Let R be a ring on which there is a left calculus of fractions (treating the ring as a category), also known as the left Ore condition on the set of non zero-divisors. Suppose that the ring of fractions Q gotten by inverting all non zero-divisors and suppose that Q is R-injective. (This happens, e.g. if the ring is a domain, but there are many other examples.) Then the functors Hom(-,R) defines a pre-duality between the category of left topological R-modules and that of R-modules. The fixed categories consist, on one hand, of those topological modules that are the kernels of continuous homomorphisms between powers of R and, on the other, of those modules that have a pure embedding into a power of R.