The valuation structure of homomorphic images of Prüfer domains
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- by Monte B. Boisen and Philip B. Sheldon PDF
- Proc. Amer. Math. Soc. 46 (1974), 335-342 Request permission
Abstract:
Let $R$ denote a Prüfer ring which is a homomorphic image of a Prüfer domain $D$. The purpose of this paper is to investigate the relationship between the valuation structure over $D$ and the valuation structure over $R$. It is shown that there exists a one-to-one correspondence between the valuations over $R$ and the valuations over $D$ centered on primes containing the kernel of the homomorphism. This correspondence is shown to be natural in the sense that the value of an element of $R$ is either infinity or the value of its pre-images under the corresponding valuation over $D$. Moreover, the value group of a valuation over $R$ is an isolated subgroup of the value group of the corresponding valuation over $D$.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 46 (1974), 335-342
- MSC: Primary 13F05
- DOI: https://doi.org/10.1090/S0002-9939-1974-0404246-2
- MathSciNet review: 0404246