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Rings with A Finitely Generated Total Quotient Ring

Published online by Cambridge University Press:  20 November 2018

John Conway Adams
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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.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 1 - 4
Copyright
Copyright © Canadian Mathematical Society 1974

References

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