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arXiv · 2209.13194

Two-sided zero product determined algebras

Žan Bajuk·Matej Brešar
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Abstract

An algebra $A$ is said to be two-sided zero product determined if every bilinear functional $\varphi:A\times A\to F$ satisfying $ \varphi(x,y)=0$ whenever $xy=yx=0$ is of the form $\varphi(x,y)=\tau_1(xy) + \tau_2(yx)$ for some linear functionals $\tau_1,\tau_2$ 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.

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Žan Bajuk, Matej Brešar. 2022-09-27. Two-sided zero product determined algebras. https://arxiv.org/abs/2209.13194

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