关于诱导映射的两个保持问题
Two Preserver Problems on Induced Maps

作者: 闫盼盼 * , 张 隽 * , 曹重光 :黑龙江大学数学科学学院,黑龙江 哈尔滨 ;

关键词: 矩阵保交换保幂等诱导映射Field Matrix Preserving Commutativity Preserving Idempotence Induced Map

摘要:
令F是一个域,Mn(F)是F上所有nχn矩阵的集合。如果一个映射f:Mn(F)→Mn(F)被定义如下,f:A=(aij)1→(fij((aij))),∀A∈Mn(F)其中{aij|i,j∈[1,2,...n]}是关于F的函数集,则称fMn(F)的由{fij}诱导的映射。如果AB=BA意味着f(A)f(B)=f(B)f(A),则f被称为保交换矩阵。如果B2=B意味着(f(B))2=f(B),则f被称为保幂等矩阵。本文我们分别刻画保域上矩阵幂等性及交换性的诱导映射。

Abstract: Let F be a field, Mn(F) be the set of alln × nmatrices over F. If a map f: Mn(F) → Mn(F) is defined by f:A=(aij)1→(fij((aij))), ∀A∈Mn(F) where {aij|i,j∈[1,2,...n]} are the set of func-tions on F, then f is called a map induced by {fij} on Mn(F). If AB = BA implies f(A)f(B) = f(B)f(A), then f is called preserving commutativity of matrices. If B2=B implies (f(B))2=f(B), then f is called preserving idempotent matrices. In this paper, we characterize induced maps preserving idempo-tence and commutativity of matrices over fields, resprectively.

文章引用: 闫盼盼 , 张 隽 , 曹重光 (2015) 关于诱导映射的两个保持问题。 理论数学, 5, 247-254. doi: 10.12677/PM.2015.55035

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