If $\mathcal{L}(R)$ is a set of left ideals defined in
any ring $R,$ we say that $R$ is $\mathcal{L}$-stable if it has stable range
1 relative to the set $\mathcal{L}(R)$. We explore $\mathcal{L}$-stability
in general, characterize when it passes to related classes of rings, and
explore which classes of rings are $\mathcal{L}$-stable for some$\mathcal{\ L}.$ Some well known examples of $\mathcal{L}$-stable rings are presented,
and we show that the Dedekind finite rings are $\mathcal{L}$-stable for a
suitable $\mathcal{L}$.
Stable range uniquely generated ring internal cancellation ring von Neumann regular ring unit-regular ring triangular matrix ring left idealtors $\mathcal{L}$-stable ring
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 5 Ocak 2021 |
Yayımlandığı Sayı | Yıl 2021 Cilt: 29 Sayı: 29 |