Browsing by Author "Kosan, Tamer"

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    Unit and Idempotent Additive Maps Over Countable Linear Transformations
    (Hacettepe Univ, Fac Sci, 2024) Gümüsel, Günselı; Kosan, Tamer; Zemlicka, Jan
    Let 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).