A ring $Q$ is usually called a right ring of fractions (or sometimes ring of quotients) for a ring $R$ if there is a homomorphism $R \to Q$ that maps some multiplicative set $S \subset R$ to invertible elements of $Q$. There are many constructions of rings of fractions (applicable in different situations and generally inequivalent), including classical, maximal, and Martindale rings of quotients.
Rings with this keyword