Published online by Cambridge University Press: 14 November 2011
Let A and B be commutative Noetherian local rings such that B contains A and B is flat and integral over A. It is shown that if M is a balanced big Cohen-Macaulay A-module (that is, every system of parameters for A is an M-sequence), then M⊗AB is a balanced big Cohen-Macaulay B-module. An example of a ring A is given such that, if B is the completion of A, then the analogous result is false in this case. This answers a question posed by Riley in the negative.