Noetherian rings between a semilocal domain and its completion

[摘要] We consider a general technique for constructing local. Noetherian integral domains. Let R be a semilocal Noetherian domain with Jacobson radical m and field of fractions K. Let y be a nonzero element of m and let R* be the (y)-adic completion of R. For elements tau(1),...,tau(s) is an element of yR* algebraically independent over K, we obtain a necessary and sufficient condition for A = K(tau(1),...,tau(s)) boolean AND R* to be simultaneously Noetherian and a directed union of localized polynomial rings in s variables over R. We specify conditions in order that excellence be preserved, and we use the construction to obtain a non-Noetherian ring A of the form K(tau) boolean AND R* which is a directed union of localized polynomial ring over R. (C) 1997 Academic Press.

[发布日期] 1997-12-15