{'fraction_non_alphanumeric': 0.023255813953488372, 'fraction_numerical': 0.0, 'mean_word_length': 4.97029702970297, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A constructive theory of minimal zero-dimensional extensions

. Chiorescu characterized the minimal zero- dimensional extensions of certain one-dimensional rings in terms of families of ideals indexed by prime ideals. In this paper we give a constructive development of these extensions, which, to achieve maximum generality, must necessarily avoid dependence on prime ideals. This forces us to develop a purely arithmetic theory. Along the way we get a characterization, in terms of the lattice of radicals of ﬁnitely generated ideals, of when a ring with primary zero-ideal has dimension at most one.