2×2 矩阵代数保持幂等的映射(英文)  

Maps on 2 × 2 matrix algebras preserving idempotence

作　　者：徐金利[1] 

机构地区：[1]黑龙江大学数学科学学院,黑龙江哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2004年第4期128-131,共4页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Science Found of China (10271021)

摘　　要：Let M2 be the algebra of all 2 × 2 matrices over a ?eld F of characteristic 2 and |F| > 2. Let P2 be the set of all idempotent matrices in M2. It is shown that if φ : M2 → M2 is an injective map such that A ? λB ∈ P2 implies φ(A) ? λφ(B) ∈ P2 for any A,B ∈ M2 and λ ∈F, then either φ is of the form φ(A) = TAT? for any A ∈ M2, or φ is of 1 the form φ(A) = TAtT? for any A ∈ M2, where T ∈ M2 is a nonsingular matrix.Let M2 be the algebra of all 2 × 2 matrices over a ?eld F of characteristic 2 and |F| > 2. Let P2 be the set of all idempotent matrices in M2. It is shown that if φ : M2 → M2 is an injective map such that A ? λB ∈ P2 implies φ(A) ? λφ(B) ∈ P2 for any A,B ∈ M2 and λ ∈F, then either φ is of the form φ(A) = TAT? for any A ∈ M2, or φ is of 1 the form φ(A) = TAtT? for any A ∈ M2, where T ∈ M2 is a nonsingular matrix. 1

关 键 词：幂等 单射 矩阵代数 

分 类 号：O151.21[理学—数学]