BL-代数的弱(相对)零化子

Weak(Relative) annihilator of BL-algebras

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。

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.