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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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Noncommutative algebras of dimension three over integral schemes
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by Rick Miranda and Mina Teicher PDF
Trans. Amer. Math. Soc. 292 (1985), 705-712 Request permission

Abstract:

In this article we describe the algebraic data which is equivalent to giving an associative, noncommutative algebra ${\mathcal {O}_X}$ over an integral $k$-scheme $Y$ (where $k$ is an algebraically closed field of characteristic $\ne 3$), which is locally free of rank $3$. The description allows us to conclude that, essentially, all such are locally upper triangular $2 \times 2$ matrices, with degenerations of a restricted form allowed.
References
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 292 (1985), 705-712
  • MSC: Primary 16A46; Secondary 16A48
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0808748-8
  • MathSciNet review: 808748