{'fraction_non_alphanumeric': 0.02217741935483871, 'fraction_numerical': 0.0, 'mean_word_length': 4.4021739130434785, '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}}
Integral domains issued from associated primes

Abstract For a property of integral domains, D is said to be an - domain if DP has the property for all associated prime ideals P of an integral domain D. Our first goal is to study some ring-theoretic properties of - domains; in particular, we investigate the property of being an - domain in the polynomial ring and the t-flat overring extension. Also we study integral domains satisfying the ascending chain condition on associated prime ideals.