Editing Injective hull (section)

===Ring structure===
In some cases, for ''R'' a subring of a self-injective ring ''S'', the injective hull of ''R'' will also have a ring structure.{{sfn|Lam|1999|loc=p. 78–80}} For instance, taking ''S'' to be a full [[matrix ring]] over a field, and taking ''R'' to be any ring containing every matrix which is zero in all but the last column, the injective hull of the right ''R''-module ''R'' is ''S''. For instance, one can take ''R'' to be the ring of all upper triangular matrices. However, it is not always the case that the injective hull of a ring has a ring structure, as an example in {{harv|Osofsky|1964}} shows.

A large class of rings which do have ring structures on their injective hulls are the [[nonsingular ring]]s.{{sfn|Lam|1999|loc=p. 366}} In particular, for an [[integral domain]], the injective hull of the ring (considered as a module over itself) is the [[field of fractions]]. The injective hulls of nonsingular rings provide an analogue of the ring of quotients for non-commutative rings, where the absence of the [[Ore condition]] may impede the formation of the [[classical ring of quotients]]. This type of "ring of quotients" (as these more general "fields of fractions" are called) was pioneered in {{harv|Utumi|1956}}, and the connection to injective hulls was recognized in {{harv|Lambek|1963}}.