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Search: MSC category 16U99 ( None of the above, but in this section )

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1. CMB 2009 (vol 53 pp. 321)

Lee, Tsiu-Kwen; Zhou, Yiqiang
 A Theorem on Unit-Regular Rings Let $R$ be a unit-regular ring and let $\sigma$ be an endomorphism of $R$ such that $\sigma (e)=e$ for all $e^2=e\in R$ and let $n\ge 0$. It is proved that every element of $R[x \mathinner;\sigma]/(x^{n+1})$ is equivalent to an element of the form $e_0+e_1x+\dots +e_nx^n$, where the $e_i$ are orthogonal idempotents of $R$. As an application, it is proved that $R[x \mathinner; \sigma ]/(x^{n+1})$ is left morphic for each $n\ge 0$. Keywords:morphic rings, unit-regular rings, skew polynomial ringsCategories:16E50, 16U99, 16S70, 16S35

2. CMB 1999 (vol 42 pp. 174)

Ferrero, Miguel; Sant'Ana, Alveri
 Rings With Comparability The class of rings studied in this paper properly contains the class of right distributive rings which have at least one completely prime ideal in the Jacobson radical. Amongst other results we study prime and semiprime ideals, right noetherian rings with comparability and prove a structure theorem for rings with comparability. Several examples are also given. Categories:16U99, 16P40, 16D14, 16N60