Communications of the
Korean Mathematical Society CKMS

A ring $R$ is called an $I_0$-ring if each left ideal not contained in the Jacobson radical $J(R)$ contains a non-zero idempotent. If, in addition, idempotents can be lifted modulo $J(R)$, $R$ is called an $I$-ring or a potent ring. We study whether these properties are inherited by some related rings. Also, we investigate the structure of potent rings.

Keywords: potent rings, idempotents, Jacobson radical, formal power series ring

MSC numbers: Primary 16D10, 16D60