Amalgamations of Domains

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*TS is a domain.