| 剩余格及有界psBCK-代数成为布尔代数的充要条件 |
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| 引用本文： | 王丽丽,张小红.剩余格及有界psBCK-代数成为布尔代数的充要条件[J].模糊系统与数学,2010,24(5). |
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| 作者姓名： | 王丽丽 张小红 |
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| 作者单位： | 宁波大学,数学系,浙江,宁波,315211 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 研究了一般剩余格(未必可换)与布尔代数的关系,给出剩余格成为布尔代数的一系列充要条件.同时,进一步将这些结果推广到只含有蕴涵运算的有界psBCK-代数中,证明了在一定条件下由psBCK-代数可诱导出有界格且构成布尔代数.
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| 关 键 词： | 剩余格 布尔代数 psMTL-代数 psBCK-代数 |
Necessary and Sufficient Conditions for Residuated Lattice and Bounded psBCK-algebra to be Boolean algebra |
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| WANG Li-li,ZHANG Xiao-hong.Necessary and Sufficient Conditions for Residuated Lattice and Bounded psBCK-algebra to be Boolean algebra[J].Fuzzy Systems and Mathematics,2010,24(5). |
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| Authors: | WANG Li-li ZHANG Xiao-hong |
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| Institution: | WANG Li-li,ZHANG Xiao-hong(Department of Mathematics,Ningbo University,Ningbo 315211,China) |
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| Abstract: | The relationship between general residuated lattices(may be not commutative) and the Boolean algebras,some necessary and sufficient conditions for a residuated lattice to be a Boolean algebra are established.Moreover,these results are generalized to bounded psBCK-algebras which only have implication operators. |
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| Keywords: | Residuated Lattice Boolean Algebra psMTL Algebra psBCK-algebra |
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