Commutative Nil-Neat Group Rings

Let R be a ring and G a group. We establish a rather curious necessary and sufficient condition for the commutative group ring RG to be nil-neat only in terms of R,G and their sections. This somewhat extends two recent results established by McGovern et al. in (J. Algebra Appl., 2015) and by Udar et al. in (Commun. Algebra, 2017), related to commutative nil-clean and neat group rings, respectively.