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Article Unit and Idempotent Additive Maps Over Countable Linear Transformations(Hacettepe Univ, Fac Sci, 2024) Gümüsel, Günselı; Kosan, Tamer; Zemlicka, JanLet 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).Article Citation - WoS: 2Citation - Scopus: 2On fusible rings(Taylor & Francis inc, 2023) Gumusel, Guenseli; Kosan, M. Tamer; Zemlicka, JanA ring R is called left fusible if every nonzero element is the sum of a left zero-divisor and a non-left zero-divisor, and R is called uniquely left fusible if for any a is an element of R there exists a unique left zero-divisor z such that a - z is non-left zero-divisor. We show that a left fusible ring R is uniquely left fusible if and only if either R is a domain or R has a unique non-left zero-divisor element.
