Amalgamations of Domains

✍ Scribed by S.Peter Farbman

• Book ID: 102574399
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 103 KB
• Volume: 221
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.7944

✦ Synopsis

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# S is a domain.