具有标准对合的低秩环
Rings of low rank with a standard involution
摘要：
考虑任意基环R上的低秩R-代数的分类问题。我们首先根据代数的度对代数进行分类，并将度为2的代数类与具有标准对合的代数类联系起来。然后，我们研究了一类例外环的程度2发生在每个rank n >= 1，并表明，他们本质上刻画所有代数的程度2和rank 3。
英文摘要：
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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