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- W1991310667 abstract "Let M n ( R ) be the algebra of all n × n matrices over a unital commutative ring R with 2 invertible, V be an R -module. It is shown in this article that, if a symmetric bilinear map { · , · } from M n ( R ) × M n ( R ) to V satisfies the condition that { u , u } = { e , u } whenever u 2 = u , then there exists a linear map f from M n ( R ) to V such that { x , y } = f ( x ∘ y ) , ∀ x , y ∈ M n ( R ) . Applying the main result we prove that an invertible linear transformation θ on M n ( R ) preserves idempotent matrices if and only if it is a Jordan automorphism, and a linear transformation δ on M n ( R ) is a Jordan derivation if and only if it is Jordan derivable at all idempotent points." @default.
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- W1991310667 date "2011-12-01" @default.
- W1991310667 modified "2023-10-17" @default.
- W1991310667 title "Idempotent elements determined matrix algebras" @default.
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- W1991310667 doi "https://doi.org/10.1016/j.laa.2011.05.002" @default.
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