Abstract
An algebra A is said to be two-sided zero product determined if every bilinear functional φ:A×A→F satisfying φ(x,y)=0 whenever xy=yx=0 is of the form φ(x,y)=τ1(xy)+τ2(yx) for some linear functionals τ1,τ2 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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