On algebras which are locally in codimensionone
Authors:
S. M. Bhatwadekar, Amartya K. Dutta and Nobuharu Onoda
Journal:
Trans. Amer. Math. Soc. 365 (2013), 44974537
MSC (2010):
Primary 13F20; Secondary 14R25, 13E15
Published electronically:
January 9, 2013
MathSciNet review:
3066764
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Abstract: Let be a Noetherian normal domain. Call an algebra ``locally in codimensionone'' if is a polynomial ring in one variable over for every heightone prime ideal in . We shall describe a general structure for any faithfully flat algebra which is locally in codimensionone and deduce results giving sufficient conditions for such an algebra to be a locally polynomial algebra. We also give a recipe for constructing algebras which are locally in codimensionone. When 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 algebra , which is locally in codimensionone, to be Krull and a further condition for to be Noetherian. The results are used to construct intricate examples of faithfully flat algebras locally in codimensionone which are Noetherian normal but not finitely generated.
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 A.K. Dutta, On bundles of affine morphisms, J. Math. Kyoto Univ. 35(3) (1995), 377385. MR 1359003 (96j:14011)
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 A.K. Dutta and N. Onoda, On finite generation of subalgebras of , J. Algebra 320 (2008), 5780. MR 2417977 (2009c:13049)
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 P. Eakin and W. Heinzer, A cancellation problem for rings, in: Conference on Commutative Algebra, in: Lecture Notes in Math., vol. 311, SpringerVerlag, 1973, pp. 6177. MR 0349664 (50:2157)
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Additional Information
S. M. Bhatwadekar
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
Address at time of publication:
Bhaskaracharya Pratishthana, 56/14, Erandwane, Damle Path, Off Law College Road, Pune, 411 004, India
Email:
smb@math.tifr.res.in, smbhatwadekar@gmail.com
Amartya K. Dutta
Affiliation:
StatMath Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108, India
Email:
amartya@isical.ac.in
Nobuharu Onoda
Affiliation:
Department of Mathematics, University of Fukui, Fukui 9108507, Japan
Email:
onoda@ufukui.ac.jp
DOI:
http://dx.doi.org/10.1090/S00029947201305619X
Keywords:
Codimensionone,
faithfully flat,
finite generation,
retraction,
complete local,
Krull domain,
divisorial ideal,
symbolic power
Received by editor(s):
November 12, 2010
Received by editor(s) in revised form:
April 28, 2011
Published electronically:
January 9, 2013
Article copyright:
© Copyright 2013
American Mathematical Society
