Weakly commuting maps on the set of rank-1 matrices

Abstract

Let be a natural number. Let be the ring of all matrices over an arbitrary field . In the present paper, we will find the description of all additive mappings such that for all , where ( and are matrices units). As an application we will characterize all additive maps such that for all , where represents the set formed by all rank-1 matrices of . Precisely, we will show that for all if and only if for all .

Keywords:

• Weakly commuting maps
• commuting maps
• rank-1 matrices
• functional identities

AMS Subject Classifications:

• 16R60

Notes

No potential conflict of interest was reported by the authors