1. CMB 2017 (vol 60 pp. 861)
 Wang, Long; CastroGonzalez, Nieves; Chen, Jianlong

Characterizations of Outer Generalized Inverses
Let $R$
be a ring and $b, c\in R$.
In this paper, we give some characterizations of the $(b,c)$inverse,
in terms of the direct sum decomposition, the annihilator and
the invertible elements.
Moreover, elements with equal $(b,c)$idempotents related to
their $(b, c)$inverses are characterized, and the reverse order
rule for the $(b,c)$inverse is considered.
Keywords:$(b, c)$inverse, $(b, c)$idempotent, regularity, imagekernel $(p, q)$inverse, ring Categories:15A09, 16U99 

2. CMB 2016 (vol 59 pp. 461)
 Ara, Pere; O'Meara, Kevin C.

The Nilpotent Regular Element Problem
We use George Bergman's recent normal form for universally adjoining
an inner inverse to show that, for general rings, a nilpotent
regular element $x$ need not be unitregular.
This contrasts sharply with the situation for nilpotent regular
elements in exchange rings (a large class of rings), and for
general rings when all powers of the nilpotent element $x$ are
regular.
Keywords:nilpotent element, von Neumann regular element, unitregular, Bergman's normal form Categories:16E50, 16U99, 16S10, 16S15 

3. CMB 2009 (vol 53 pp. 321)
 Lee, TsiuKwen; Zhou, Yiqiang

A Theorem on UnitRegular Rings
Let $R$ be a unitregular 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, unitregular rings, skew polynomial rings Categories:16E50, 16U99, 16S70, 16S35 

4. 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 
