  A ring $R$ is said to be $n$-clean if every element can be written as a sum
of an idempotent and $n$ units. The class of these rings contains clean ring
and $n$-good rings in which each element is a sum of $n$ units. In this paper,
we show that for any ring $R$, the endomorphism ring of a free $R$-module of
rank at least 2 is 2-clean and that the ring $B(R)$ of all $\omega\times
\omega$ row and column-finite matrices over any ring $R$ is 2-clean. Finally,
the group ring $RC_{n}$ is considered where $R$ is a local ring. \vskip 0.5cm
{\bf Key words:}\quad 2-clean rings, 2-good rings, free modules, row and
column-finite matrix rings, group rings.
