On Rings of Fractions
Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 425-430
Voir la notice de l'article provenant de la source Cambridge University Press
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
@article{10_4153_CMB_1970_079_1,
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/}
}
[1] 1. Artin, E. and Tate, J., A note on finite ring extensions,J. Math. Soc. Japan 3 (1951), 74-77. Google Scholar
[2] 2. Gilmer, D., The pseudo-radical of a commutative ring, Pacific J. Math. 19 (1966), 275-284. Google Scholar
[3] 3. Warner, S., Compact noetherian rings, Math. Ann. 141 (1960)5 161-170. Google Scholar
[4] 4. Zariski, O. and Samuel, P., Commutative algebra I, II, Van Nostrand, Princeton, N.J., 1958. Google Scholar
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