Geodesic
A Non-Trivial Ring with Non-Rational Injective Hull
Canadian mathematical bulletin, Tome 10 (1967) no. 2, pp. 275-282

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Several authors have investigated "rings of quotients" of a given ring R . (See, for example, Johnson [7], Johnson and Wong [8], Utumi [11], Findlay and Lambek [5], Lambek [9], and Bourbaki [2].) 
Berthiaume, P. A Non-Trivial Ring with Non-Rational Injective Hull. Canadian mathematical bulletin, Tome 10 (1967) no. 2, pp. 275-282. doi: 10.4153/CMB-1967-027-9
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     author = {Berthiaume, P.},
     title = {A {Non-Trivial} {Ring} with {Non-Rational} {Injective} {Hull}},
     journal = {Canadian mathematical bulletin},
     pages = {275--282},
     year = {1967},
     volume = {10},
     number = {2},
     doi = {10.4153/CMB-1967-027-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-027-9/}
}
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