Abstract
We consider a general technique for constructing local Noetherian integral domains. LetRbe a semilocal Noetherian domain with Jacobson radicalmand field of fractionsK. Letybe a nonzero element ofmand letR* be the (y)-adic completion ofR. For elements τ1,…,τs∈yR* algebraically independent overK, we obtain a necessary and sufficient condition forA≔K(τ1,…,τs)∩R* to be simultaneously Noetherian and a directed union of localized polynomial rings insvariables overR. We specify conditions in order that excellence be preserved, and we use the construction to obtain a non-Noetherian ringAof the formK(τ)∩R* which is a directed union of localized polynomial rings overR.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
