Power commuting additive maps on rank-k linear transformations
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...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Others |
| Language: | en_US |
| Published: |
2018
|
| Online Access: | http://ndltd.ncl.edu.tw/handle/yhr8a7 |
| Summary: | 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 .
|
|---|