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.References
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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