On algebras which are locally A1 in codimension-one

• 資料種別: 文書・図像類
• タイトル: On algebras which are locally A1 in codimension-one
• 著者・編者: BHATWADEKAR, S. M.; DUTTA, AMARTYA K.; ONODA, NOBUHARU
• 著者標目: BHATWADEKAR, S. M.; DUTTA, AMARTYA K.; ONODA, NOBUHARU
• 出版事項: American Mathematical Society
• 出版年月日等: 2013-06
• 出版年（W3CDTF）: 2013-06
• タイトル（掲載誌）: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
• 巻号年月日等（掲載誌）: 365 9
• 掲載巻: 365
• 掲載号: 9
• 掲載ページ: 4497-4537
• 本文の言語コード: eng
• 件名標目: Codimension-one; faithfully flat; finite generation; retraction; complete local; Krull domain; divisorial ideal; symbolic power
• 対象利用者: 一般
• 一般注記: 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.
• 一次資料へのリンクURL: https://u-fukui.repo.nii.ac.jp/?action=repository_action_common_download&item_id=23007&item_no=1&attribute_id=22&file_no=1
• オンライン閲覧公開範囲: 限定公開
• 関連情報（DOI）: 10.1090/S0002-9947-2013-05619-X
• 連携機関・データベース: 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
• 提供元機関・データベース: 福井大学 : 福井大学学術機関リポジトリ