| 效应代数的表示及弱表示 |
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| 引用本文： | 张巧卫,曹怀信,陆玲.效应代数的表示及弱表示[J].西北大学学报,2012(2):198-202. |
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| 作者姓名： | 张巧卫 曹怀信 陆玲 |
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| 作者单位： | 榆林学院数学与应用数学系;陕西师范大学数学与信息科学学院;西安陆军学院军事运筹教研室 |
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| 基金项目： | 国家自然科学基金资助项目(10571113;10871224) |
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| 摘 要： | 目的给出效应代数的表示及弱表示的定义,研究幂集和布尔代数的可表示性。方法用效应代数表示的定义及效应代数中态射的性质得出结论。结果证明了E是可表示的,则E是弱可表示的;若E是弱可表示的,则由E到Hilbert空间效应代数的强态射诱导的效应代数是可表示的;布尔代数格同构和效应代数同构是一致的。结论幂集作为一个效应代数是可表示的,任何有限布尔代数是可表示的效应代数。
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| 关 键 词： | 效应代数 单调态射 强态射 表示 弱表示 |
Representation and weak representation of effect algebras |
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| ZHANG Qiao-wei,CAO Huai-xin,LU Ling.Representation and weak representation of effect algebras[J].Journal of Northwest University(Natural Science Edition),2012(2):198-202. |
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| Authors: | ZHANG Qiao-wei CAO Huai-xin LU Ling |
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| Institution: | 1.Department of Mathematics and Applied Mathematics,Yulin University,Yulin 719000,China; 2.College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China; 3.Section of Military Operation Research,Xi′an Military Academy,Xi′an 710108,China) |
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| Abstract: | Aim To introduce the definitions of representation and weak representation of an effect algebra and study the representability of the power set and Boolean algebra.Methods By using the definition of representation of effect algebra and the characters of morphisms to obtain the results.Results If E is representable,then it is weak representable.If E is a weak representable effect algebra,then the effect algebra induced by a strong morphism from E into a Hilbert space effect algebra is representable.Lattice isomorphism coincides with effect algebra isomorphism for Boolean algebras.Conclusion It is proved that the power set and every finite Boolean algebra can be represented. |
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| Keywords: | effect algebra monomorphism strong morphism representation weak representation |
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