Geodesic
On Rings of Fractions
Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 425-430

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Let R be a commutative Noetherian ring with identity, and let M be a fixed ideal of R. Then, trivially, ring multiplication is continuous in the ilf-adic topology. Let S be a multiplicative system in R, and let j = js: R → S-1R, be the natural map. One can then ask whether (cf. Warner [3, p. 165]) S-1R is a topological ring in ihe j(M)-adic topology. In Proposition 1, I prove this is the case if and only if M ⊂ p(S), where Hence S -1 R is a topological ring for all S if and only if M ⊂ p*(R), where 
Davison, T. M. K. On Rings of Fractions. Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 425-430. doi: 10.4153/CMB-1970-079-1
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     author = {Davison, T. M. K.},
     title = {On {Rings} of {Fractions}},
     journal = {Canadian mathematical bulletin},
     pages = {425--430},
     year = {1970},
     volume = {13},
     number = {4},
     doi = {10.4153/CMB-1970-079-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-079-1/}
}
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