Gumusel, GunseliKosan, M. TamerZemlicka, JanDepartment of Social Sciences for University wide Courses2024-07-052024-07-05202402651-477X10.15672/hujms.11876082-s2.0-85193010888https://doi.org/10.15672/hujms.1187608https://hdl.handle.net/20.500.14411/2328Let V be a countably generated right vector space over a field F and a E End(V F ) be a shift operator. We show that there exist a unit u and an idempotent e in End(V F ) such that 1 - u, a - u are units in End(V F ) and 1 - e, a - e are idempotents in End(V F ) . We also obtain that if D is a division ring D % Z 2 , Z 3 and V D is a D -module, then for every alpha E End(V D ) there exists a unit u E End(V D ) such that 1 - u, alpha - u are units in End(V D ) .eninfo:eu-repo/semantics/openAccess. unitshift operatoridempotent matrixtripotent matrixsemilocal ringdivision ringArticle532305313WOS:001225022700001