w 1. Introduction In an earlier paper [4], the author gave necessary and sufficient conditions for a topological left Ore domain to be topologically embeddable in its field of quotients. In w 2, we use the results of [4] to give a new proof of Warner's theorem on open embeddings [7]. In w 3, we prove that a commutative domain A which is a Q-ring with continuous quasi-inversion has a finer non-discrete ring topology in which the multiplicative semigroup A* = A- {0} is embeddable in its quotient group. We also prove that an infinite compact Hausdorff commutative domain has a finer non-discrete ring topology in which it is openly embeddable in its quotient field. These theorems generalize the following theorem of Rothman [5]. Theorem. A compact Hausdorff commutative domain A with identity has a finer non-discrete topology on A* for which A* is embeddable in its group of quotients. For completeness, we state the following result due to Tamari [6]. Theorem T. A commutative cancellative topological semigroup S is embeddable in its group of quotients if and only if its topology is invariantly uniformisable.