| 条件交半格中的相对极大滤子 |
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| 引用本文： | 路玲霞,王群.条件交半格中的相对极大滤子[J].模糊系统与数学,2011,25(2):66-70. |
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| 作者姓名： | 路玲霞 王群 |
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| 作者单位： | 1. 石家庄经济学院,数理学院,河北,石家庄,050031
2. 河北科技大学,理学院,河北,石家庄,050018 |
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| 基金项目： | 国家自然科学基金资助项目，河北省自然科学基金资助项目，河北省教育厅基金资助项目，石家庄经济学院校立基金资助项目 |
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| 摘 要： | 引入偏序集的相对极大滤子的概念,证明在任意条件交半格中一个滤子是相对极大滤子当且仅当它是滤子格的完全交不可约元.一个格是分配的当且仅当每一个相对极大滤子都是素滤子.随后研究了Heyting代数中相对极大滤子的刻画,最后定义和研究了完全并既约生成格.
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| 关 键 词： | 条件交半格 相对极大滤子 完全交不可约元 完备并既约生成格 |
Relative Maximal Filters in Conditional Semilattices |
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| LU Ling-xia,WANG Qun.Relative Maximal Filters in Conditional Semilattices[J].Fuzzy Systems and Mathematics,2011,25(2):66-70. |
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| Authors: | LU Ling-xia WANG Qun |
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| Institution: | LU Ling-xia1,WANG Qun2(1.School of Mathematics and Science,Shijiazhuang University of Economics,Shijiazhuang 050031,China,2.School of Science,Hebei University of Science and Technology,Shijiahuznag 050018,China) |
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| Abstract: | On any posets,the relative maximal filters are introduced and studied.It is shown that in any conditional semilattice,a filter is relative maximal iff it is a completely meet-irreducible element of the filter-lattice;a lattice is distributive iff each relative maximal fiter is prime.A characterization of relative maximal filters in Heyting algebras is given.Lastly,completely join-irreducible generated lattices are introduced and strudied. |
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| Keywords: | Conditinal Semilattice Relative Maximal Filter Completely Meet-ireducible Element Completely Join-irreducible Generated Lattice |
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