Let $V$ be a countably generated right vector space over a field $F$ and $\sigma\in End(V_F)$ be a shift operator. We show that there exist a unit $u$ and an idempotent $e$ in $End(V_F)$ such that $1-u,\sigma-u$ are units in $End(V_F)$ and $1-e,\sigma-e$ are idempotents in $End(V_F)$. We also obtain that if $D$ is a division ring $D\ncong \mathbb Z_2, \mathbb Z_3 $ and $V_D$ is a $D$-module, then for every $\alpha\in End(V_D)$ there exists a unit $u\in End(V_D)$ such that $1-u,\alpha-u$ are units in $End(V_D)$.
unit shift operator idempotent matrix tripotent matrix semilocal ring division ring
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Erken Görünüm Tarihi | 10 Ocak 2024 |
Yayımlanma Tarihi | 23 Nisan 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 53 Sayı: 2 |