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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The preparation theorem and the freeness of $A[[X]]/I$
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by S. H. Cox PDF
Proc. Amer. Math. Soc. 61 (1976), 227-231 Request permission

Abstract:

Let $I$ be a nonzero ideal of $A[[X]]$, the ring of formal power series over a commutative Noetherian ring $A$. These are equivalent: (i) $I$ is generated by a single series $f = {a_0} + {a_1}X + \ldots$ such that for some $s,\;{a_s}$ is a unit, the first $s$ coefficients ${a_0}, \ldots ,{a_{s - 1}}$ of $f$ lie in the Jacobson radical of $A$ and $A$ is complete in the adic topology defined by the ideal they generate. (ii) $A[[X]]/I$ is a free $A$-module.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 61 (1976), 227-231
  • MSC: Primary 14D15; Secondary 13B05, 13J05, 14B10
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0427317-5
  • MathSciNet review: 0427317