Henselian valuations and orderings of a commutative ring
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Abstract:
The purpose of this paper is to investigate the interplay between henselian valuations and orderings (or semiorderings) of a ring. As a main result, it is proved that for a henselian valuation $v$ on a ring $R$, the following statements are equivalent: (1) $v$ is compatible with every semiordering of $R$; (2) $v$ is compatible with every ordering of $R$; (3) Every real prime ideal of $R$ is contained in the core of $v$.References
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Additional Information
- Guangxing Zeng
- Affiliation: Department of Mathematics, Nanchang University, Jiangxi Province, Nanchang 330047, People’s Republic of China
- Email: zenggx@ncu.edu.cn
- Received by editor(s): October 23, 2005
- Published electronically: September 18, 2006
- Additional Notes: This work was partially supported by a National Key Basic Research Project of China (Grant No. 2004CB318003).
- Communicated by: Bernd Ulrich
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 929-938
- MSC (2000): Primary 13J30; Secondary 13J25, 12J15, 12D15
- DOI: https://doi.org/10.1090/S0002-9939-06-08726-0
- MathSciNet review: 2262892