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Henselian valuations and orderings of a commutative ring |
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| Authors: | Guangxing Zeng |
| Institution: | Department of Mathematics, Nanchang University, Jiangxi Province, Nanchang 330047, People's Republic of China |
| 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  . |
| Keywords: | Commutative ring henselian valuation ordering real prime ideal |
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