Power commuting additive maps on rank-k linear transformations

• Main Authors: Chou, Ping-Han, 周秉漢
• Other Authors: Liu, Cheng-Kai
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/yhr8a7

碩士 === 國立彰化師範大學 === 數學系 === 106 === Let M be a right vector space over a division ring D and let End ) ( D M be the ring of all D-linear transformations from M into M . Suppose that R is a dense subring of End ) ( D M consisting of finite rank transformations and RRf : is an additive map satisfying ) ()( )()( x fxxxf xmxm  for every rank-k transformation R x , where k is a fixed integer with D Mk dim1  and 1)( xm is an integer depending on x. Then there exist ) (DZ  and an additive map I DZR ) (:   such that ) ()( x xxf   for all R x , where I denotes the identity transformation on M .