[For the entire collection see Zbl 0676.00006.]
This note is concerned with the behavior of the Gelfand-Kirillov dimension under localizations with respect to the multiplicatively closed subsets of regular elements s in A for which \(sA=As\). Such elements are called normal elements. It is shown that if s is a normal element of A which determines an automorphism of A and if there is a commutative subalgebra B invariant under this automorphism such that A is finitely generated as a right B[s]-module, then the Gelfand-Kirillov dimension does not increase under localization by s. An element s in A is called local normal if s is a normal element determining a locally algebraic automorphism of A. It is then shown that if S is a multiplicatively closed subset of A consisting of local normal elements, then S in an Ore set and the Gelfand-Kirillov dimension of A localized at S is the same as that of A. The article concludes with examples of a pathological behavior of Gelfand-Kirillov dimension under constructions of the above type.