A Theorem on Unit-Regular Rings

[摘要] Let $R$ be a unit-regular ring and let $sigma $ be an endomorphism of$R$ such that $sigma (e)=e$ for all $e^2=ein R$ and let $nge 0$. Itis proved that every element of $R[x mathinner;sigma]/(x^{n+1})$ isequivalent to an element of the form $e_0+e_1x+dots +e_nx^n$, wherethe $e_i$ are orthogonal idempotents of $R$. As an application, it isproved that $R[x mathinner; sigma ]/(x^{n+1})$ is left morphic for each$nge 0$.

[学科分类] 数学（综合）

[关键词] morphic rings;unit-regular rings;skew polynomial rings