| 环上的模糊理想幂格及其强截集诱导的格 |
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| 引用本文： | 李倩,辛小龙,花秀娟.环上的模糊理想幂格及其强截集诱导的格[J].模糊系统与数学,2010,24(5). |
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| 作者姓名： | 李倩 辛小龙 花秀娟 |
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| 作者单位： | 西北大学,数学系,陕西,西安,710127 |
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| 基金项目： | 陕西省自然科学基金资助项目，陕西省教育厅专项科研基金资助项目 |
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| 摘 要： | 给出了环上模糊理想幂格的概念,得到相关性质。进而由环上模糊理想强截集诱导出格,讨论了它不是分配格,但为模格。同时,将环上升为主理想环,得到了模糊理想乘积的强截集等于强截集的乘积,且都为环的理想。最后,讨论了Boolean环的模糊子集为模糊理想与其伴随构成交半格的关系。
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| 关 键 词： | 格 环的模糊理想 环上的模糊理想幂格 强截集 |
Fuzzy Ideal Power Lattice and Induced lattice of Fuzzy Ideal Strong Cut Set of a Ring |
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| LI Qian,XIN Xiao-long,HUA Xiu-juan.Fuzzy Ideal Power Lattice and Induced lattice of Fuzzy Ideal Strong Cut Set of a Ring[J].Fuzzy Systems and Mathematics,2010,24(5). |
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| Authors: | LI Qian XIN Xiao-long HUA Xiu-juan |
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| Institution: | LI Qian,XIN Xiao-long,HUA Xiu-juan(Department of Mathematics,Xibei University,Xi'an 710127,China) |
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| Abstract: | In this paper,we define a fuzzy ideal power lattice of a ring and obtain relative properties.At the same time,we use strong cut set of fuzzy ideal of a ring to construct lattice,which is a modular lattice but not a distributive lattice.When the ring is stepped up principle ideal ring,we prove that strong cut set of fuzzy ideal's product is equal to strong cut set's product.Meanwhile,they are ideals of a ring.At last,we prove the relation between fuzzy ideal of Boolean ring and cross-semi lattice formed by a... |
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| Keywords: | Lattice Fuzzy Ideal of Ring Fuzzy Ideal Power Lattice of Ring Strong Cut Set |
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