Abstract
Let be positive integers such that for and let denote the algebra of matrices over a field for . Let be the tensor product of . We obtain a structural characterization of additive maps satisfying for all , where and is the standard matrix unit in for . In particular, we show that is an additive map commuting on if and only if there exist a scalar and an additive map such that for all . As an application, we classify additive maps satisfying for all . Here, denotes the set of rank matrices in and each is a fixed integer such that when and for .
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