Generic formal fibers of polynomial ring extensions (Q1880980)

It is shown that if \((R,M)\) is a universally catenary local Noetherian domain such that the dimension of the generic formal fiber ring of \(R[X]_{(M,X)}\) is \(\dim(R)\), then the dimension of the generic formal fiber ring of \(R\) is \(\dim(R)-1\). It also is shown by a counterexample that the converse does not hold.