| 赋范BCK-代数(英文) |
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| 引用本文： | 彭家寅.赋范BCK-代数(英文)[J].数学进展,2011(4). |
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| 作者姓名： | 彭家寅 |
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| 作者单位： | 四川省高等学校数值仿真重点实验室;内江师范学院数学与信息科学学院; |
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| 基金项目： | Supported by NSFC(No.11071178); the special item of Key Laboratory of Education Bureau of Sichuan Province(No.2006ZD050) |
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| 摘 要： | 引入了BCK-代数的范数与距离的概念,给出了赋范BCK-代数的一些基本性质,证明了赋范BCK-代数的同构(同态)像和原像仍是赋范BCK-代数,研究了BCK-代数与BCK-代数笛卡儿之间的赋范性质关系.并且引入了赋范BCK-代数的点列极限概念,研究了极限的相关性质.讨论了有界赋范BCK-代数的与模糊BCK-代数的关系.
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| 关 键 词： | 范数 赋范BCK-代数 距离 极限 模糊子代数 |
Normed BCK-algebras |
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| PENG Jiayin.Normed BCK-algebras[J].Advances in Mathematics,2011(4). |
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| Authors: | PENG Jiayin |
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| Institution: | PENG Jiayin (1.Key Laboratory of Numerical Simulation of Sichuan Province,Neijiang,Sichuan,641100,P.R. China,2.College of Math,and Inform.Sci.,Neijiang Normal University,P.R.China) |
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| Abstract: | The notions of norm and distance in BCK-algebras are introduced,and some basic properties in normed BCK-algebras are given.It is obtained that the isomorphic (homomorphic) image and inverse image of a normed BCK-algebra are still normed BCK-algebras.The relations of normed properties between BCK-algebra and Cartesian product of BCK-algebras are investigated.The limit notion of sequence of points in normed BCK-algebras is introduced,and its related properties are investigated,the relations between bounded no... |
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| Keywords: | norm normed BCK-algebra distance limit fuzzy subalgebra |
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