On additive transformations preserving a multiplicative matrix function

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• 作者：Baodong Zheng ; Yang Zhang
• 关键词：Preserve ; Multiplicative function
• 刊名：Applied Mathematics and Computation
• 出版年：2007
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 June 2007
• 卷：189
• 期：2
• 页码：1402-1409
• 文件大小：162 K

摘要

Let M_n(K) be the ring of all n×n matrices over a division ring K, and f be a multiplicative matrix function from M_n(K) to a multiplicative Abelian group with zero G{0} (f(AB)=f(A)f(B),A,BM_n(K)). We call an additive transformation on M_n(K) preserves a multiplicative matrix function f, if f((A))=f(A),AM_n(K). In this paper, we characterize all additive surjective transformations on M_n(K) over any division ring K (chK≠2) that leave a non-trivial multiplicative matrix function invariant. Applications to several related preservers are considered.