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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Classification of the Tor-algebras of codimension four almost complete intersections
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by Andrew R. Kustin PDF
Trans. Amer. Math. Soc. 339 (1993), 61-85 Request permission

Abstract:

Let $(R,m,k)$ be a local ring in which $2$ is a unit. Assume that every element of $k$ has a square root in $k$. We classify the algebras $\operatorname {Tor}_ \bullet ^R(R/J,k)$ as $J$ varies over all grade four almost complete intersection ideals in $R$ . The analogous classification has already been found when $J$ varies over all grade four Gorenstein ideals [21], and when $J$ varies over all ideals of grade at most three [5, 30]. The present paper makes use of the classification, in [21], of the Tor-algebras of codimension four Gorenstein rings, as well as the (usually nonminimal) ${\text {DG}}$-algebra resolution of a codimension four almost complete intersection which is produced in [25 and 26].
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 339 (1993), 61-85
  • MSC: Primary 13D03; Secondary 13C05, 13C40
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1132435-7
  • MathSciNet review: 1132435