Two-sided zero product determined algebras
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.
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