{'fraction_non_alphanumeric': 0.02188183807439825, 'fraction_numerical': 0.0, 'mean_word_length': 4.3882352941176475, '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}}
Amalgamations of Domains

Abstract The question of whether the amalgamated free product of two domains is itself a domain is considered. Some results analogous to group-theoretic approaches to the zero-divisor conjecture are proved. A condition is introduced that guarantees that the amalgam will be a domain. If, for example, R is a polynomial ring over the domain T , then only minimal restrictions on how T embeds in S guarantee that R ∗ T S is a domain.