标题： 关于二维向量空间上对称非退化双线性型的约当代数的可换同位体 显示英文标题

标题： On commutative isotopes of Jordan algebra of a symmetric bilinear nondegenerate form on a two-dimensional vector space

摘要： 在本文中，我们研究了特征不等于 2 的代数闭域上的简单幺元交换三维代数。 证明了每个幂零秩为 2 的简单幺元交换三维代数都与二维向量空间上对称非退化双线性型的 Jordan 代数同胚。 显示英文摘要

摘要： In the article we study the simple unital communitative three-dimensional algebras over an algebraically closed field of characteristic not equal to 2. It is proved that every simple unital communitative three-dimensional algebra of nil-rank 2 is isotopic to Jordan algebra of a symmetric bilinear nondegenerate form on a two-dimensional vector space.