| 半环中赋值与序的相容性 |
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| 引用本文： | 肖水晶,万雁飞.半环中赋值与序的相容性[J].南昌大学学报(理科版),2012,36(1):11-16. |
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| 作者姓名： | 肖水晶 万雁飞 |
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| 作者单位： | 南昌大学数学系,江西南昌,330031 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 在交换半环范畴中,研究赋值与序之间的相容性。通过引进赋值的半截口,这样一个事实被证明:半环的一个赋值具有一个半截口,只要该赋值的值幺半群是一个群。基于此事实,建立了如下主要结果:对于半环S的一个赋值v,v是S的一个实赋值当且仅当v与S的某个序相容。
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| 关 键 词： | 半环 赋值 实赋值 正锥 亚正锥 序 半截口 实素理想 |
Compatibility between orderings and valuations in commutative semiring |
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| XIAO Shui-jing
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WAN Yan-fei.Compatibility between orderings and valuations in commutative semiring[J].Journal of Nanchang University(Natural Science),2012,36(1):11-16. |
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| Authors: | XIAO Shui-jing WAN Yan-fei |
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| Affiliation: | (Department of Mathematics,Nanchang University,Nanchang 330031,China) |
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| Abstract: | The compatibility between orderings and valuations was investigated in a commutative semiring.By introducing the notion of semisections for valuations on a commutative semiring,it proved that the valuation on a commutative semiring possesses a semisection,as long as its value monoid is a group.Based on this fact,the following main result was established:for a valuation on a commutative semiring v,is real if and only if it is compatible with some ordering of. |
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| Keywords: | semiring valuation real valuation positive precone positive cone ordering compatibility semisection real prime ideal |
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