首页|Multiplicative Derivations on Rank-s Matrices for Relatively Small s
Multiplicative Derivations on Rank-s Matrices for Relatively Small s
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NETL
NSTL
万方数据
维普
In this paper,we describe multiplicative derivations on the set of all rank-s matrices of Mn(K)over a field K with a relatively small integer s.Concretely,for fixed integers n,s satisfying 1 ≤ s ≤ n/2 and n ≥ 2,we prove that if a map δ:Mn(K)→ Mn(K)satisfies δ(xy)=δ(x)y+xδ(y)for any two rank-s matrices x,y ∈ Mn(K),then there exists a derivation D of Mn(K)such that δ(x)=D(x)for each rank-k matrix x ∈ Mn(K)with 0 ≤ k ≤ s.As an application,we prove that a multiplicative derivation on a special subset of Mn(K)must be a derivation.
NETL
NSTL
万方数据
维普
