Algebra retracts and Poincar�-series

Abstract

Let R⊂A be a local inclusion of noetherian local rings. Assume that R is an algebra retract of A with the local retraction mapping p:A→R. Let M be an R-module of finite type. Considering M as A-module via p we get PMA=PRAPMR (Th. 1), where PNS denotes the Poincareseries of an S-module N. This result is used to give a simple proof of Th. 1 in [2], Also an application to fibre products of rings is given (Th. 2), generalizing slightly a result due to A. Dress and H. Kramer, see [1].