@Article{CMR-26-4,
author = {Weixing, Chen and Shuying, Cui},
title = {On $π$-Regularity of General Rings},
journal = {Communications in Mathematical Research },
year = {2010},
volume = {26},
number = {4},
pages = {313--320},
abstract = {<p style="text-align: justify;">A general ring means an associative ring with or without identity. An
idempotent $e$ in a general ring $I$ is called left (right) semicentral if for every $x ∈ I$, $xe = exe (ex = exe)$. And $I$ is called semiabelian if every idempotent in $I$ is left
or right semicentral. It is proved that a semiabelian general ring $I$ is $π$-regular if
and only if the set $N(I)$ of nilpotent elements in $I$ is an ideal of $I$ and $I/N(I)$ is
regular. It follows that if $I$ is a semiabelian general ring and $K$ is an ideal of $I$,
then $I$ is $π$-regular if and only if both $K$ and $I/K$ are $π$-regular. Based on this we
prove that every semiabelian GVNL-ring is an SGVNL-ring. These generalize several
known results on the relevant subject. Furthermore, we give a characterization of a
semiabelian GVNL-ring.</p>},
issn = {2707-8523},
doi = {https://doi.org/2010-CMR-19128},
url = {https://global-sci.com/article/81916/on-p-regularity-of-general-rings}
}