| IMTL代数上的素布尔滤子格 |
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| 引用本文： | 刘贤江,张家录. IMTL代数上的素布尔滤子格[J]. 数学理论与应用, 2008, 28(3): 61-64 |
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| 作者姓名： | 刘贤江 张家录 |
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| 作者单位： | 湘南学院数学系,郴州 423000 |
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| 摘 要： | 本文研究IMTL代数M上的索布尔滤子的运算性质。令FB（M）为膨上全体素布尔滤子集，FB（M）=FB（M）∪{φ}，通过在集合FB（M）引进格并、交运算和逆序对合对应，证明了FB（M）构成一个拟布黎代数。进一步在FB（M）可定义一个伴随对，证明FB（M）也构成一个剩余格。
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| 关 键 词： | 剩余格 IMTL代数 素滤子 布尔滤子 拟布尔代数 |
The Prime Boolean Filter Lattices of IMTL Algebras |
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| Liu Xianjiang Zhang Jialu. The Prime Boolean Filter Lattices of IMTL Algebras[J]. Mathematical Theory and Applications, 2008, 28(3): 61-64 |
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| Authors: | Liu Xianjiang Zhang Jialu |
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| Affiliation: | Liu Xianjiang Zhang Jialu (Department d Mathematics,Xiangnan University, Chenzhou,423000) |
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| Abstract: | This paper focuses on the operatiom about prime boolean fitter of IMTL algebra M.Let FB（M） be the set of all prime boolean fitter of IMTL algebra M and FB（M）= FB（M）∪{φ} ,The V - operation, ∧ - operation, onter- revers- ing involution correspondence anti adjoint pair （×）,→） on FB（M） are defined.The conclusions that ,FB（M） defined as above is a quasi- boolean algebra and is also a residuated lattice are obtained. |
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| Keywords: | Residuated lattice IMTL algebra Prime filter Boolean fi lter Quasi-boolean algebra |
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