Additive maps on rank-s matrices. Issue 4 (3rd April 2017)

• Record Type: Journal Article
• Authors: Xu, Xiaowei; Liu, Hanchao
• Is Part Of: Linear & multilinear algebra. Volume 65:Issue 4(2017)
• Page Start: 806
• Page End: 812
• Publication Date: 2017-04-03
• Subjects: Additive maps -- rank-s matrices; 15A03 -- 15A23; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2016.1202887
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : Let be the ring of all matrices over a field with . In this paper, it is proved that a map is additive if and only if for all rank- s matrices, where s is a fixed positive integer such that, which has been verified to be true for the case in [Xu X, Pei Y, Yi X. Additive maps on invertible matrices. Linear Multilinear Algebra. 2016;64:1283–1294]. Also, an example is provided showing that the conclusion will be incorrect if .