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

DOI:
https://doi.org/10.1090/S0002-9939-06-08726-0

Published electronically:
September 18, 2006

MathSciNet review:
2262892

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Abstract | References | Similar Articles | Additional Information

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 on a ring , the following statements are equivalent: (1) is compatible with every semiordering of ; (2) is compatible with every ordering of ; (3) Every real prime ideal of is contained in the core of .

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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:
https://doi.org/10.1090/S0002-9939-06-08726-0

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.