Let S be a ring with identity, and M a unitary left S-module. If defined, K-dim s (M) and G-dim s (M) denote the Krull dimension and the Gabriel dimension of M, respectively, and K-dim(5") and G-dim(S') stand for the left Krull dimension and the left Gabriel dimension of the ring S.In what follows, we let L always be a semimaximal left ideal (i.e., the intersection of finitely many maximal left ideals) of S; its idealizer in S will always be denoted by R, i.e. R = {s e S \ Ls £ L). In [5] J. C. Robson found the structures of JR and S remarkably closely linked, and it is the purpose of this note to point out a few more similarities. In particular, Robson showed that K-dim(.R) = K-dim(S) if S is left noetherian, and we shall establish this result in general, provided R or S has left Krull dimension. Also, G-dim(R) = G-dim(.S) will be shown, provided either side exists.For some basic information concerning Krull dimension and Gabriel dimension we refer to [2], [3], and [4]. LEMMA 1. Let N be an R-submodule of the left S-module M. If the left S-module M/LN has finite uniform dimension, then N/LN is a semisimple artinian left R-module.