Zero product determined matrix algebras
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Matej Brešar; Mateja Grašič; Juana Sánchez Ortega
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Article
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2009
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Elsevier Science
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English
⚖ 166 KB
Let A be an algebra over a commutative unital ring C. We say that A is zero product determined if for every C-module X and every bilinear map {•, •} : A × A → X the following holds: if {x, y} = 0 whenever xy = 0, then there exists a linear operator T such that {x, y} = T (xy) for all x, y ∈ A. If we