Illinois Journal of Mathematics

Rings of low rank with a standard involution

John Voight

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We consider the problem of classifying (possibly noncommutative) $R$-algebras of low rank over an arbitrary base ring $R$. We first classify algebras by their degree, and we relate the class of algebras of degree 2 to algebras with a standard involution. We then investigate a class of exceptional rings of degree 2 which occur in every rank $n ≥ 1$ and show that they essentially characterize all algebras of degree 2 and rank 3.

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Illinois J. Math., Volume 55, Number 3 (2011), 1135-1154.

First available in Project Euclid: 29 May 2013

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Primary: 16G30: Representations of orders, lattices, algebras over commutative rings [See also 16Hxx] 11E20: General ternary and quaternary quadratic forms; forms of more than two variables 16W10: Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]


Voight, John. Rings of low rank with a standard involution. Illinois J. Math. 55 (2011), no. 3, 1135--1154. doi:10.1215/ijm/1369841800.

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