## Illinois Journal of Mathematics

### Rings of low rank with a standard involution

John Voight

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 29 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1369841800

Digital Object Identifier
doi:10.1215/ijm/1369841800

Mathematical Reviews number (MathSciNet)
MR3069299

Zentralblatt MATH identifier
1351.16039

#### Citation

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

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