  The m-weak group inverse was recently studied in the literature. The purpose
of this paper is to investigate new properties of this generalized inverse for
ring elements. We introduce the m-weak group decomposition for a ring element
and prove that it coincides with its m-weak group invertibility. We present the
equivalent characterization of the m-weak group inverse by using a polar-like
property. The relations between m-weak group inverse and core-EP inverse are
also established. These give some new properties of the weak group inverse for
complex matrices and ring elements.
