It is proved that there exists an NI ring R over which the polynomial ring R[x] is not an NLI ring. This answers an open question of Qu and Wei (Stud. Sci. Math. Hung., 51(2), 2014) in the negative. Moreover a sufficient condition of R[x] to be an NLI ring is included for an NLI ring R.
Amitsur, S. A., Radicals of polynomial rings, Canad. J. Math., 8 (1956), 355–361.
Amitsur S. A., 'Radicals of polynomial rings' (1956) 8Canad. J. Math.: 355-361.
Amitsur S. A.Radicals of polynomial ringsCanad. J. Math.19568355361)| false