R_0-代数中的广义相对零化子

Generalized Relative Annihilators in R_0-Algebras

首先,利用滤子的扩张方法在R_0-代数中引入相对零化子的概念,并结合滤子的概念提出广义相对零化子的概念,证明R_0-代数中广义相对零化子仍是滤子;其次,利用广义相对零化子刻画素滤子,并讨论相对零化子与广义相对零化子的关系;最后,基于R_0-代数中的两个给定元,给出一个以广义相对零化子为对象的满足并无穷分配律的完备剩余格结构.

Firstly, using the methods of extended filters, we introduced the concept of the relative annihilator in R0-algebras, and proposed the concept of the generalized relative annihilator combined with the concept of filters, and it was proved that the generalized relative annihilators in R0-algebras were still filters. Secondly, we described the prime filters by using the generalized relative annihilator, and discussed the relationship between the relative annihilators and generalized relative annihilators. Finally, based on two given elements in R0-algebras, we gave a complete residuated lattice structure which satisfied join-infinite distributive law in the family of generalized relative annihilators.