A study of BL-algebras by UC-filters

In this article, with the aim of further investigating BL-algebras, the concepts of Unity Co-annihilator-filters (UC-filters) is introduced and discussed. Also, for the faster study of UC-filters in BL-algebras, some equivalent conditions are obtained, and (with some examples) it is shown that these filters have differences. In addition, we consider several additional conditions imposed on UC-filters and prime filters and establish links between them. So, we get relationships between these types of filters and prime filters in BL-algebras. Finally, the form of all UC-saturated ∨-closed subsets of a G- algebras (by the concept of UC-saturated ∨-closed subsets) is stated.