Bulletin of the
Korean Mathematical Society BKMS

Let $R$ be an associative ring with identity and $J(R)$ be the Jacobson radical of $R$. In this paper we investigate the generalization of the Jacobson radical of $R$, $J^{*}(R)$ say. Also we study the rings that $J^{*}(R)=J(R)$.

Keywords: Jacobson radical, matrix ring, non-left-invertible, stable range one

MSC numbers: 16D70, 16N20