タイトル（掲載誌）TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
一般注記出版タイプ： AO
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.
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）