| 格蕴涵代数中的格蕴涵代数方程 |
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| 引用本文： | 潘小东,徐扬,张青.格蕴涵代数中的格蕴涵代数方程[J].西南交通大学学报,2005,40(6):842-845. |
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| 作者姓名： | 潘小东 徐扬 张青 |
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| 作者单位： | 西南交通大学理学院,四川,成都,610031 |
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| 基金项目： | 国家自然科学基金资助项目(6047022) |
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| 摘 要： | 根据逻辑代数方程理论,提出了格蕴涵代数方程的概念.讨论了格蕴涵代数L中的几种基本类型的一元格蕴涵代数方程,给出了方程的可解性判别条件.在此基础之上,证明了方程的解集构成L的凸子格.
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| 关 键 词： | 格蕴涵代数 格蕴涵代数方程 凸子格 可解性 解集 |
| 文章编号： | 0258-2724（2005）06-0842-04 |
| 收稿时间： | 2004-04-30 |
| 修稿时间： | 2004-04-30 |
Lattice Implication Algebraic Equations in Lattice Implication Algebras |
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| PAN Xiao-dong,XU Yang,ZHANG Qing.Lattice Implication Algebraic Equations in Lattice Implication Algebras[J].Journal of Southwest Jiaotong University,2005,40(6):842-845. |
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| Authors: | PAN Xiao-dong XU Yang ZHANG Qing |
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| Institution: | School of Science, Southwest jiaotong University, Chengdu 610031, China |
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| Abstract: | According to the theory about logic algebraic equation,the notion of lattice implication algebraic equation was proposed.Some typical one varialbe lattice implication algebraic equations in lattice implication algebras L were discussed.The necessary and sufficient conditions for existance of solutions for the equations were presented.Based on the discussions,it was proved that the solution sets of the equations are convex sublattices of L. |
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| Keywords: | lattice implication algebra lattice implication algebraic equation convex sublattice solvability solution set |
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