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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Henselian valuations and orderings of a commutative ring


Author: Guangxing Zeng
Journal: Proc. Amer. Math. Soc. 135 (2007), 929-938
MSC (2000): Primary 13J30; Secondary 13J25, 12J15, 12D15
Published electronically: September 18, 2006
MathSciNet review: 2262892
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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$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08726-0
PII: S 0002-9939(06)08726-0
Keywords: Commutative ring, henselian valuation, ordering, real prime ideal
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.