%0 Journal Article
%T Extensions of square stable range one
%A Huanyin Chen
%A Marjan Sheibani
%J Mathematics
%D 2014
%I arXiv
%X An ideal $I$ of a ring $R$ is square stable if $aR+bR=R$ with $a\in I$ and $b\in R$ implies that $a^2+by$ is invertible in $I$ for some $y\in I$. We prove that an exchange ideal $I$ of a ring $R$ is square stable if and only if for any $a\in I$, $a^2\ in J(R)$ implies that $a\in J(R)$, if and only if every regular element in $I$ is strongly regular.
%U http://arxiv.org/abs/1409.3973v1