  A ring $R$ is said to be clean if each element of $R$ can be written as the
sum of a unit and an idempotent. $R$ is said to be weakly clean if each element
of $R$ is either a sum or a difference of a unit and an idempotent, and $R$ is
said to be feebly clean if every element $r$ can be written as $r=u+e_1-e_2$,
where $u$ is a unit and $e_1,e_2$ are orthogonal idempotents. Clearly clean
rings are weakly clean rings and both of them are feebly clean. In a recent
article (J. Algebra Appl. 17 (2018), 1850111(5 pages)), McGoven characterized
when the group ring $\mathbb Z_{(p)}[C_q]$ is weakly clean and feebly clean,
where $p, q$ are distinct primes. In this paper, we consider a more general
setting. Let $K$ be an algebraic number field, $\mathcal O_K$ its ring of
integers, $\mathfrak p\subset \mathcal O$ a nonzero prime ideal, and $\mathcal
O_{\mathfrak p}$ the localization of $\mathcal O$ at $\mathfrak p$. We
investigate when the group ring $\mathcal O_{\mathfrak p}[G]$ is weakly clean
and feebly clean, where $G$ is a finite abelian group, and establish an
explicit characterization for such a group ring to be weakly clean and feebly
clean for the case when $K=\mathbb Q(\zeta_n)$ is a cyclotomic field or
$K=\mathbb Q(\sqrt{d})$ is a quadratic field.
