In a recent paper [1], Brown, Hajarnavis and MacEacharn have considered non-commutative Noetherian local rings of finite global dimension which are integral over their centres. For such a ring Rthey have shown:(i) R is a prime ring whose Krull and global dimensions coincide;(ii) R = ∩ R_P where p runs through the set of rank one primes of the centre of R, and each R_p is hereditary;(iii) the centre of R is a Krull domain.