Abstract
The main goal of this paper is to introduce and research co-annihilators and $$\alpha $$ -filters in residuated lattices. We characterize $$\alpha $$ -filters in terms of co-annihilators. Also, we answer the open problem which appeared in Haveshki and Mohamadhasani (J Intell Fuzzy Syst 28:373–382, 2015). We prove that the lattice of all $$\alpha $$ -filters in a residuated lattice forms a complete Heyting algebra. Finally, we investigate some topological properties of space of prime $$\alpha $$ -filters and give necessary and sufficient conditions for the space to become a $$T_{1}$$ space and Hausdorff space.
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