Rings of low rank with a standard involution

2010/03/18 by Voight, John · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1003.3512

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.

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