Multiplicative Derivations on Rank-s Matrices for Relatively Small s

Author:

Xu Xiaowei1,Xie Baochuan1,Wang Yanhua2,Zhao Zhibing3

Affiliation:

1. College of Mathematics, Jilin University, Changchun 130012, China

2. School of Mathematics, Shanghai Key Laboratory of Financial Information Technology, Shanghai University of Finance and Economics, Shanghai 200433, China

3. School of Mathematical Sciences, Anhui University, Hefei 230601, China

Abstract

In this paper, we describe multiplicative derivations on the set of all rank-[Formula: see text] matrices of [Formula: see text] over a field [Formula: see text] with a relatively small integer [Formula: see text]. Concretely, for fixed integers [Formula: see text], [Formula: see text] satisfying [Formula: see text] and [Formula: see text], we prove that if a map [Formula: see text] satisfies [Formula: see text] for any two rank-[Formula: see text]matrices [Formula: see text], [Formula: see text], then there exists a derivation [Formula: see text] of [Formula: see text] such that [Formula: see text] for each rank-[Formula: see text] matrix [Formula: see text] with [Formula: see text]. As an application, we prove that a multiplicative derivation on a special subset of [Formula: see text] must be a derivation.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Algebra and Number Theory

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