Closed ideals with the zero-dimensional root set in certain rings of holomorphic functions

Abstract

In the paper one considers closed ideals with a zero-dimensional root set in certain rings H of holomorphic functions, defined in a pseudo-Euclidean domain ~ ~ . One establishes that under certain additional assumptions on such an ideal ~ , the ideal localizes, i.e., it coincides with the set of functions ~e H , whose germs, at all points ~ ~ ~, are generated over the ring of series convergent at ~ by the germs of the elements of the ideal 3 9