| Quantale中的素根定理 |
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| 引用本文： | 汪开云.Quantale中的素根定理[J].模糊系统与数学,2011,25(2). |
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| 作者姓名： | 汪开云 |
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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： | 国家自然科学基金资助项目 |
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| 摘 要： | 在Quantale中引入了m系的概念,利用m系讨论了Quantale中素理想和半素理想之间的关系.在此基础上证明了当Q是可换Quantale时,Id(Q)是空间式Quantale当且仅当Q中的任一理想都是半素理想.最后把环和序半群中的素根定理推广到Quantak中,得到了Quantale中的素根定理.
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| 关 键 词： | 素理想 半素理想 m系 理想的根 |
Prime Radical Theorem in Quantales |
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| WANG Kai-yun.Prime Radical Theorem in Quantales[J].Fuzzy Systems and Mathematics,2011,25(2). |
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| Authors: | WANG Kai-yun |
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| Institution: | WANG Kai-yun(College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,China) |
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| Abstract: | In this paper,the concept of m system in a quantale Q is introduced.We use the m system to discuss the relations between prime ideals and semiprime ideals in the quantale Q.Based on these,we prove that Id(Q) is a spatial quantale if and only if every ideal in Q is semiprime,if Q is a commutive quantale.Finally,the prime radical theorem in rings and ordered semigroups is generalized in quantales.Hence we obtain the prime radical theorem in quantales. |
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| Keywords: | Quantale |
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