Geodesic
On the Complete Ring of Quotients
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 285-288

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

In [2: p. 415], P. Gabriel proves that if R is a ring with 1 and S is a non-empty multiplicative set such that 0∉S, then S-1R exists if and only if for every pair (a, s)∈R×S, there is a pair (b, t)∈R×S such that at=sb and if s1a=0 for some s 1 in S then as2 =0 for some s 2 in S. The purpose of this note is to give a self contained elementary proof of Gabriel’s result. 
Koh, Kwangil. On the Complete Ring of Quotients. Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 285-288. doi: 10.4153/CMB-1974-056-9
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[1] 1. Findlay, G. D. and Lamhek, J., A generalized ring of quotients I, Canadian Math. Bull., Vol. l, no. 2, May 1958. Google Scholar

[2] 2. Gabriel, P., Des categories abeliennes, Bull. Soc. Math., France 90 (1962), 325-448. Google Scholar

[3] 3. Johnson, R. E., The extended centralizer of a ring over a module, Proc. Amer. Math. Soc. 2 (1951), 891-895. Google Scholar

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