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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Flat analytic extensions
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by Ana M. D. Viola-Prioli PDF
Trans. Amer. Math. Soc. 202 (1975), 385-404 Request permission

Abstract:

This paper is concerned, in the first place, with the conditions to be imposed on an ideal $I$ of the power series ring in one indeterminate $A[[x]]$ ($A$ noetherian) in order that the analytic extension $B = A[[x]]/I$ be a flat $A$-module. Also the relationship between the projectivity and finiteness of $B$ is found when the content of $I$ (the ideal of $A$ generated by the coefficients of all power series in $I$) equals $A$. A generalization of this result to the power series ring in any finite number of indeterminates is obtained when $A$ is local, noetherian of Krull $\dim \geq 1$, and under certain restrictions on $I$, for the global case but only for domains. Finally, a contribution to the problem of the finiteness of $I$ when $A[[x]]/I$ is a flat analytic extension is given for $A$ a local ring, not necessarily noetherian.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 202 (1975), 385-404
  • MSC: Primary 13J05
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0389891-0
  • MathSciNet review: 0389891