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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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The homological dimensions of symmetric algebras
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by James E. Carrig PDF
Trans. Amer. Math. Soc. 236 (1978), 275-285 Request permission

Abstract:

Let D be a Dedekind domain and M a rank-one torsion-free D-module. An analysis of $A = {S_D}(M)$, the symmetric algebra of M, yields the following information: Theorem. (1) Tor-dim $A \leqslant 2\;and\; = 1\;iff\;M = K$, the quotient field of D; (2) A is coherent; (3) Global $\dim A = 2$. For higher rank modules coherence is not assured and only rough estimates of the dimensions are found. On the other hand, if ${S_D}(M)$ is a domain of global dimension two, then M has rank one but the dimension of D may be two. If D is local of dimension two then $M = K$.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 236 (1978), 275-285
  • MSC: Primary 13D05
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0457425-0
  • MathSciNet review: 0457425