| 预Girard quantale及其性质的研究 |
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| 引用本文： | 赵彬,韩胜伟.预Girard quantale及其性质的研究[J].陕西师范大学学报,2007,35(4):1-4,27. |
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| 作者姓名： | 赵彬 韩胜伟 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安710062 |
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| 基金项目： | 国家自然科学基金;陕西师范大学校科研和教改项目 |
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| 摘 要： | 研究了预Girard quantale的性质以及在预Girard quantale上核映射与余核映射之间的关系，简化了理想余核的定义，讨论了理想余核的一些性质，给出了右侧幂等quantale上所有理想余核的具体刻画．得到了预Girard quantale是Girard quantale的充要条件．证明了任意Quantale都可以嵌入到预Girard quantale中，并且在预Girard quantale上核映射与理想余核是一一对应关系．
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| 关 键 词： | 完备格 预Grard quantale 核映射 理想余核 |
| 文章编号： | 1672-4291（2007）04-0001-04 |
| 收稿时间： | 2007-06-14 |
| 修稿时间： | 2007年6月14日 |
Researches on pre-Girard quantale and its properties |
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| ZHAO Bin,HAN Sheng-wei.Researches on pre-Girard quantale and its properties[J].Journal of Shaanxi Normal University: Nat Sci Ed,2007,35(4):1-4,27. |
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| Authors: | ZHAO Bin HAN Sheng-wei |
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| Abstract: | Some of the properties of pre-Girard quantale and the relation between nuclei and conuclei on pre-Girard quantale are studied, the definition of the ideal conucleus is simplified, some of the properties of ideal conuclei are discussed, and the concrete constructions of ideal conuclei on right-sided and idempotent quantales are given. A sufficient and necessary condition for a pre-Girard quantale to be a Girard quantale is obtained. It is proved that every quantale can be embedding into a pre-Girard quantale, and nuclei and ideal conuclei on pre-Girard quantale are in one-to-one correspondence. |
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| Keywords: | Quantale Girard quantale |
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