Overring properties of $G$-domains
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- by Revati Ramaswamy and T. M. Viswanathan PDF
- Proc. Amer. Math. Soc. 58 (1976), 59-66 Request permission
Abstract:
A commutative domain $R$ is called a strong $G$-domain if every overring between $R$ and the quotient field $K$ of $R$ is of the form $R[1/t]$ for some nonzero element $t$ of $R$. After characterizing valuation rings which are strong $G$-domains, the authors show that $R$ is a strong $G$-domain if and only if it is a finite intersection of valuation rings each of which is a strong $G$-domain. Using some results of R. W. Gilmer, Jr., the authors identify the strong $G$-domains in the class of all Prüfer domains. They reprove via Krull domains the theorem characterizing Noetherian $G$-domains, a result first proved by Artin and Tate. The authors also raise some relevant questions on related overring properties of $G$-domains.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 58 (1976), 59-66
- MSC: Primary 13G05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0407005-1
- MathSciNet review: 0407005