Bhatwadekar, S.M. ; Gupta, Neena
(2012)
*The structure of a Laurent polynomial fibration in n variables*
Journal of Algebra, 353
(1).
pp. 142-157.
ISSN 0021-8693

Full text not available from this repository.

Official URL: http://doi.org/10.1016/j.jalgebra.2011.11.032

Related URL: http://dx.doi.org/10.1016/j.jalgebra.2011.11.032

## Abstract

Bass, Connell and Wright have 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 paper we prove a corresponding structure theorem for a ring A which is a locally Lau�rent polynomial algebra in n variables over an integral domain R, viz., we show that A is isomorphic to an R-algebra of the form (Sym_{R} (Q ))[I ^{−1}], where Q is a direct sum of n finitely generated projective R-modules of rank one and I is a suitable invertible ideal of the symmetric algebra Sym_{R} (Q ). Further, we show that any faithfully flat algebra over a Noetherian normal domain R, whose generic and codimension-one fibres are Laurent polynomial algebras in n variables, is a locally Laurent polynomial algebra in n variables over R.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Polynomial Algebra; Symmetric Algebra; Laurent Polynomial Algebra; Codimension-One; Fibre Ring. |

ID Code: | 121208 |

Deposited On: | 13 Jul 2021 04:47 |

Last Modified: | 13 Jul 2021 04:47 |

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