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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Noncommutative algebras of dimension three over integral schemes


Authors: Rick Miranda and Mina Teicher
Journal: Trans. Amer. Math. Soc. 292 (1985), 705-712
MSC: Primary 16A46; Secondary 16A48
MathSciNet review: 808748
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0808748-8
PII: S 0002-9947(1985)0808748-8
Article copyright: © Copyright 1985 American Mathematical Society