Geodesic
Topological Rings of Quotients
Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1228-1233

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

We investigate here the notion of a topological ring of quotients of a topological ring with respect to an arbitrary Gabriel (idempotent) filter of right ideals. We describe the topological ring of quotients first as a subring of the algebraic ring of quotients, and then show it is a topological bicommutator of a topological injective R-module. Unlike R. L. Johnson in [6] and F. Eckstein in [2] we do not always make the ring an open subring of its ring of quotients. This would exclude examples such as C(X), the ring of continuous real-valued functions on a compact space, and its ring of quotients as described in Fine, Gillman and Lambek [3]. 
Schelter, William. Topological Rings of Quotients. Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1228-1233. doi: 10.4153/CJM-1974-116-4
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