Unit and idempotent additive maps over countable linear transformations

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Gümüşel G., KOŞAN M. T., Žemlička J.

Hacettepe Journal of Mathematics and Statistics, cilt.53, sa.2, ss.305-313, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.15672/hujms.1187608
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.305-313
  • Anahtar Kelimeler: division ring, idempotent matrix, semilocal ring, shift operator, tripotent matrix, unit
  • Gazi Üniversitesi Adresli: Evet

Özet

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).