Seminar

The multiplicity of a local ring R is its most fundamental invariant. For example, it tells us how singular the ring is. The multiplicity is computed from the limit as n goes to infinity of the length of R modulo the nth power of its maximal ideal. Many other multiplicity like invariants naturally occur in commutative algebra. We discuss a number of naturally occurring limits of this type, and show that in very general rings, such limits always exist.