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

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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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