Jaffard ring

In mathematics, a Jaffard ring is a type of ring, more general than a Noetherian ring, for which Krull dimension behaves as expected in polynomial extensions. They are named for Paul Jaffard who first studied them in 1960.

Formally, a Jaffard ring is a ring R such that the polynomial ring

where "dim" denotes Krull dimension. A Jaffard ring that is also an integral domain is called a Jaffard domain.

The Jaffard property is satisfied by any Noetherian ring R, so examples of non-Jaffardian rings are quite difficult to find. Nonetheless, an example was given in 1953 by Abraham Seidenberg: the subring of

consisting of those formal power series whose constant term is rational.