Abstract: Firstly, using the methods of extended filters, we introduced the concept of the relative annihilator in R0\|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.

Key words: R₀-algebras, relative annihilator, generalized relative annihilator, joininfinite distributive law, complete residuated lattice