Chris Schafhauser, Department of Pure Mathematics, University of Waterloo
“Noncommutative localisation”
If R is a commutative ring and x ∈ R is not a zero divisor, we can form a ring S = R[1/x] containing R such that x is invertible in R. This is called localisation, and the process R R[1/x] preserves nice homological and ring-theoretic properties. Things aren’t so nice for noncommutative rings — in fact there are many different ways to “localise” a noncommutative ring. Our goal now is to detail the Ore ring of fractions as it appears in Lam’s second volume, and emphasize its properties.
MC 5403