| BL-代数的弱（相对）零化子 |
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| 引用本文： | 孟彪龙,辛小龙,杨永伟. BL-代数的弱（相对）零化子[J]. 计算机工程与应用, 2016, 52(10): 27-30 |
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| 作者姓名： | 孟彪龙 辛小龙 杨永伟 |
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| 作者单位： | 1.西安科技大学 理学院，西安 7100542.西北大学 数学系，西安 710127 |
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| 摘 要： | 基于格的相对零化子概念提出了[BL-]代数的弱相对零化子概念。讨论了弱相对零化子的基本性质，证明了弱相对零化子是[BL-]代数的滤子，给出了弱相对零化子的表示定理。进一步提出了弱零化子概念，给出了零化子等价于弱零化子的充要条件，刻画了[BL-]代数全体滤子集的结构。结论为今后研究[BL-]代数的弱广义相对零化子提供了基础。
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| 关 键 词： | BL-代数 滤子 零化子 弱相对零化子 弱零化子 |
Weak(Relative) annihilator of BL-algebras |
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| MENG Biaolong,XIN Xiaolong,YANG Yongwei. Weak(Relative) annihilator of BL-algebras[J]. Computer Engineering and Applications, 2016, 52(10): 27-30 |
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| Authors: | MENG Biaolong XIN Xiaolong YANG Yongwei |
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| Affiliation: | 1.College of Science, Xi’an University of Science and Technology, Xi’an 710054, China2.Department of Mathematics, Northwest University, Xi’an 710127, China |
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| Abstract: | Based on the relative annihilator of lattices, the weak relative annihilator of [BL-algebras] is introduced. In this paper, some basic properties of a weak relative annihilator are studied, a weak relative annihilator being a filter of [BL-]algebras is proven, and a representation theorem of a weak relative annihilator is also provided. Moreover, a weak annihilator is introduced, the necessary and sufficient conditions of a annihilator is equivalent to a weak annihilator be given. Simultaneously, the structure of the set of all filters of [BL-algebras] is characterized. The work in this paper will provide a basis for studying weak generalized relative annihilator of[BL-algebras] in future. |
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| Keywords: | BL-algebras filter annihilator weak relative annihilator weak annihilator |
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