Geodesic
Rings with A Finitely Generated Total Quotient Ring
Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 1-4

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

Let R be a commutative ring with non-zero identity and let K be the total quotient ring of R. We call R a G-ring if K is finitely generated as a ring over R. This generalizes Kaplansky′s definition of G-domain [5].Let Z(R) be the set of zero divisors in R. Following [7] elements of R—Z(R) and ideals of R containing at least one such element are called regular. Artin-Tate's characterization of Noetherian G-domains [1, Theorem 4] carries over with a slight adjustment to characterize a Noetherian G-ring as being semi-local in which every regular prime ideal has rank one. 
Rings with A Finitely Generated Total Quotient Ring. Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 1-4. doi: 10.4153/CMB-1974-001-x
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[1] 1. Artin, E. and Tate, J., A note on finite ring extensions, J. Math. Soc. Japan 3 (1951), 74-77. MR 13. Google Scholar

[2] 2. Davis, E., Overrings of commutative rings H, Amer. Math. Soc. Trans. 110 (1964), 196-212. MR 28 #111. Google Scholar

[3] 3. Davison, T. M. K., On rings of fractions, Canada. Math. Bull. 13-4 (1970), 425-430. Google Scholar

[4] 4. Goldman, O., Hilbert rings and the Hilbert Nullstellensatz, Math. Z. 54 (1951), 136-146. MR 13. Google Scholar

[5] 5. Kaplansky, I., Commutative Rings, Allyn and Bacon Inc., Boston, 1970. Google Scholar

[6] 6. Nagata, M., Local Rings, Interscience Publishers, London, 1962. Google Scholar

[7] 7. Zariski, O. and Samuel, P., Commutative Algebra, Volume I, D. Van Nostrand Co., Inc., New York, 1958. Google Scholar

[8] 8. Zariski, O. and Samuel, P., Commutative Algebra, Volume II, D. Van Nostrand Co. Inc., New York 1958. Google Scholar

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