Many authors have studied the problem of determining the linear operators, on the n×n matrix algebra M<sub>n</sub>（R） over a commutative R, which preserve idempotent matrices （see Refs. [1]—[4]）....Many authors have studied the problem of determining the linear operators, on the n×n matrix algebra M<sub>n</sub>（R） over a commutative R, which preserve idempotent matrices （see Refs. [1]—[4]）. In this note, we make a start on the noncommutative case. If R and R<sub>1</sub> are division rings and their characteristic numbers are not 2 and their centers are the same field F. Let T denote an F-linear operator which maps M<sub>n</sub>（R） into M<sub>n</sub>（R<sub>1</sub>） where M<sub>n</sub>（R）展开更多
Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple ...Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.展开更多
文摘Many authors have studied the problem of determining the linear operators, on the n×n matrix algebra M<sub>n</sub>（R） over a commutative R, which preserve idempotent matrices （see Refs. [1]—[4]）. In this note, we make a start on the noncommutative case. If R and R<sub>1</sub> are division rings and their characteristic numbers are not 2 and their centers are the same field F. Let T denote an F-linear operator which maps M<sub>n</sub>（R） into M<sub>n</sub>（R<sub>1</sub>） where M<sub>n</sub>（R）
基金The NSF (10571114) of Chinathe Natural Science Basic Research Plan (2005A1) of Shaanxi Province of China
文摘Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.
