Gümüsel, GünselıKosan, TamerZemlicka, JanDepartment of Social Sciences for University wide Courses2024-07-052024-07-0520241303-50102651-477X10.15672/hujms.11876082-s2.0-85193010888https://doi.org/10.15672/hujms.1187608https://search.trdizin.gov.tr/en/yayin/detay/1235506/unit-and-idempotent-additive-maps-over-countable-linear-transformationsLet V be a countably generated right vector space over a field F and σ ∈ End(VF ) be a shift operator. We show that there exist a unit u and an idempotent e in End(VF ) such that 1−u,σ−u are units in End(VF) and 1−e,σ−e are idempotents in End(VF). We also obtain that if D is a division ring D Z2, Z3 and VD is a D-module, then for every α ∈ End(VD) there exists a unit u ∈ End(VD) such that 1−u,α−u are units in End(VD).eninfo:eu-repo/semantics/openAccessUnitShift OperatorIdempotent MatrixTripotent MatrixSemilocal RingDivision RingArticleQ3Q3532305313WOS:00122502270000112355060