Geodesic
On Ring Properties of Injective Hulls1)
Canadian mathematical bulletin, Tome 7 (1964) no. 3, pp. 405-413

Voir la notice de l'article provenant de la source Cambridge University Press

Several authors have investigated "rings of quotients" of a given ring R. Johnson showed that if R has zero right singular ideal, then the injective hull of RR may be made into a right self injective,- regular (in the sense of von Neumann) ring (see [7] and [12]). In articles by Utumi [10], Findlay and Lambek [6], and Bourbaki [2], various structures which correspond to sub-modules of the injective hull of R are made into rings in a natural manner, in [8], Lambek points out that in each of these cases the rings constructed are subrings of Utumi' s maximal ring of right quotients, which is the maximal rational extension of R in its injective hull. Lambek also shows that Utumi's ring is canonically isomorphic to the bicommutator of the injective hull of RR if R has 1. It thus appears that a "natural" definition of the injective hull of RR as a ring extending module multiplication by R has been carried out only in the case that the injective hull is a rational extension of R. (See [12], [10], or [6] for various definitions of this concept.) 
Osofsky, B. L. On Ring Properties of Injective Hulls1). Canadian mathematical bulletin, Tome 7 (1964) no. 3, pp. 405-413. doi: 10.4153/CMB-1964-039-3
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