﻿ 关于诱导映射的两个保持问题

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

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.

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