Geodesic
Self-Injective Rings
Canadian mathematical bulletin, Tome 2 (1959) no. 3, pp. 167-173

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DOI

Historically, the first example of a ring of quotients was the quotient field of an integral domain. Later on, conditions were found under which a noncommutative integral domain has a quotient division ring. More recently, R.E. Johnson [4], Y. Utumi [5], and G.D. Findlay and J. Lambek [3] have discussed the existence and structure of a maximal ring of quotients of any ring.The present paper uses the methods of Findlay and Lambek to recast the results of Johnson on the quotient ring of a ring with zero singular ideal. It is also shown that such a ring has a unique left-right maximal ring of quotients. 
Wong, E.T.; Johnson, R.E. Self-Injective Rings. Canadian mathematical bulletin, Tome 2 (1959) no. 3, pp. 167-173. doi: 10.4153/CMB-1959-022-9
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     author = {Wong, E.T. and Johnson, R.E.},
     title = {Self-Injective {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {167--173},
     year = {1959},
     volume = {2},
     number = {3},
     doi = {10.4153/CMB-1959-022-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1959-022-9/}
}
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