# 域上矩阵保乘积的诱导映射Induced Maps Preserving Multiplicative Matrices over Fields

Abstract: Let F be a field, S
n(F) be the set of all n*n matrices over F. If a map f:Sn(F)→Sn(F) is defined by ∫:B=(bij)|→(fij(bij))
where {fij|i≤j∈{1,2,...,n}} is the set of functions on F, then f is called a map induced by {fij} on Sn(F). If A,B∈Sn(F) implies f(AB)=f(A)f(B), then f is called preserving multiplicative matrices. In this paper, we characterize induced maps preserving multiplicative matrices over fields.

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