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Bass-Connell-Wright had proved that any finitely presented locally
polynomial algebra in n variables over an integral domain R is isomorphic
to the symmetric algebra of a finitely generated projective R-module of
rank n. In this talk we shall describe a corresponding structure theorem
for a ring A which is a locally Laurent polynomial algebra in n variables
over an integral domain R.
We shall also mention conditions for a faithfully flat algebra to be a
locally Laurent polynomial algebra. For instance, any faithfully flat
algebra over a Noetherian normal domain R, whose generic and
codimension-one fibres are Laurent polynomial algebras
in n variables, is locally Laurent polynomial.
The results have been obtained in a joint work with S.M. Bhatwadekar.
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