An algebra A is said to be two-sided zero product determined if every bilinear functional phi : A x A &-> F satisfying phi(x, y) = 0 whenever xy = yx = 0 is of the form phi(x, y) = T-1(xy) + T-2(yx) for some linear functionals T-1, T-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. (c) 2022 Elsevier Inc. All rights reserved.
Two-sided zero product determined algebraZero product determined algebraSeparable algebraDerivation
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