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Noetherian Rings between a Semilocal Domain and Its Completion

✍ Scribed by William Heinzer; Christel Rotthaus; Sylvia Wiegand

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
364 KB
Volume
198
Category
Article
ISSN
0021-8693

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✦ Synopsis

We consider a general technique for constructing local Noetherian integral domains. Let R be a semilocal Noetherian domain with Jacobson radical m and U Ε½ . field of fractions K. Let y be a nonzero element of m and let R be the y -adic completion of R. For elements , . . . , g yR U algebraically independent over K,

U we obtain a necessary and sufficient condition for A [ K , . . . , l R to be 1 s 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 Ε½ .

U we use the construction to obtain a non-Noetherian ring A of the form K l R which is a directed union of localized polynomial rings over R.

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