论文标题
两侧零产品确定代数
Two-sided zero product determined algebras
论文作者
论文摘要
如果每个双线性功能$φ：a \ times a \ to f $ a \ $φ（x，y）= 0 $，则每次$ xy = yx = 0 $是$ $ $ $ $ $ $ $ $ $ $（x，y）= _1（xy） +τ_2（xy）$ 1 $ 1 $ 1 $ a $ a $ a $ a $ a $确定是双面零产品的确定确定的。 $ a $。我们提出了一些基本属性和等效定义，检查与一些派生的某些属性的连接，并且主要结果证明，不是划分代数的有限维简单代数是两侧零产物，并且仅在可分离时才确定。
An algebra $A$ is said to be two-sided zero product determined if every bilinear functional $φ:A\times A\to F$ satisfying $ φ(x,y)=0$ whenever $xy=yx=0$ is of the form $φ(x,y)=τ_1(xy) + τ_2(yx)$ for some linear functionals $τ_1,τ_2$ on $A$. We present some basic properties and equivalent definitions, examine connections with some properties of derivations, and as the main result prove that a finite-dimensional simple algebra that is not a division algebra is two-sided zero product determined if and only if it is separable.
