On algebras which are locally A1 in codimension-one

Material type: 文書・図像類

Author: BHATWADEKAR, S. M.ほか

Publisher: American Mathematical Society

Publication date: 2013-06

Material Format: Digital

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Note (General)：: Let R be a Noetherian normal domain. Call an R-algebra A “locally A1 in codimension-one" if RP 〓R A is a polynomial ring in one variable over RP for e...

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Material Type: 文書・図像類
Title: On algebras which are locally A1 in codimension-one
Author/Editor: BHATWADEKAR, S. M.
DUTTA, AMARTYA K.
ONODA, NOBUHARU
Author Heading: BHATWADEKAR, S. M.
DUTTA, AMARTYA K.
ONODA, NOBUHARU
Publication, Distribution, etc.: American Mathematical Society
Publication Date: 2013-06
Publication Date (W3CDTF): 2013-06
Periodical title: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
No. or year of volume/issue: 365 9
Volume: 365
Issue: 9
Pages: 4497-4537
Text Language Code: eng
Subject Heading: Codimension-one
faithfully flat
finite generation
retraction
complete local
Krull domain
divisorial ideal
symbolic power
Target Audience: 一般
Note (General): Let R be a Noetherian normal domain. Call an R-algebra A “locally A1 in codimension-one" if RP 〓R A is a polynomial ring in one variable over RP for every height-one prime ideal P in R. We shall describe a general structure for any faithfully flat R-algebra A which is locally A1 in codimensionone and deduce results giving sufficient conditions for such an R-algebra to be a locally polynomial algebra. We also give a recipe for constructing R-algebras which are locally A1 in codimension-one. When R is a normal affine spot (i.e., a normal local domain obtained by a localisation of an affine domain), we give criteria for a faithfully flat R-algebra A, which is locally A1 in codimensionone, to be Krull and a further condition for A to be Noetherian. The results are used to construct intricate examples of faithfully flat R-algebras locally A1 in codimension-one which are Noetherian normal but not finitely generated.
Access Restrictions: 限定公開
Related Material (DOI): 10.1090/S0002-9947-2013-05619-X
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 福井大学 : 福井大学学術機関リポジトリ