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Henselian valuations and orderings of a commutative ring
Author(s):
Guangxing
Zeng
Journal:
Proc. Amer. Math. Soc.
135
(2007),
929-938.
MSC (2000):
Primary 13J30;
Secondary 13J25, 12J15, 12D15
Posted:
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  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:
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
Posted:
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 of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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