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.

Key words: BL-algebras, filter, annihilator, weak relative annihilator, weak annihilator

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。

关键词: BL-代数, 滤子, 零化子, 弱相对零化子, 弱零化子