Geodesic
On Maximal Rings of Right Quotients
Canadian mathematical bulletin, Tome 5 (1962) no. 2, pp. 147-149

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Utumi has shown [3, Claim 5.1] that for a certain class of rings the associated maximal rings of right quotients are isomorphic to the endomorphism rings of modules over division rings. We shall prove a generalization of this theorem and then show how it is obtained as a corollary. The following proofs do not depend on Utumi's paper; instead, they make extensive use of results proved in [1]. The terminology and notations employed here are the same as in [1].I wish to thank Dr. B. Banaschewski for his suggestions and helpful criticism.LEMMA: If J is a left ideal with zero left annihilator in a ring R then a maximal ring of right quotients of R is also a maximal ring of right quotients of J. 
Christensen, Joanne. On Maximal Rings of Right Quotients. Canadian mathematical bulletin, Tome 5 (1962) no. 2, pp. 147-149. doi: 10.4153/CMB-1962-016-8
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     title = {On {Maximal} {Rings} of {Right} {Quotients}},
     journal = {Canadian mathematical bulletin},
     pages = {147--149},
     year = {1962},
     volume = {5},
     number = {2},
     doi = {10.4153/CMB-1962-016-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1962-016-8/}
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