%0 Journal Article %T On the Class of Subsets of Residuated lattice which induces a Congruence Relation %J Journal of Algebra and Related Topics %I University of Guilan %Z 2345-3931 %A Harizavi, H. %D 2019 %\ 06/01/2019 %V 7 %N 1 %P 1-12 %! On the Class of Subsets of Residuated lattice which induces a Congruence Relation %K Residuated lattice %K Filter %K Complement-closed %K Congruence Relation %R 10.22124/jart.2019.11333.1119 %X In this manuscript,  we study the class of special subsets connected with a  subset in a residuated lattice and investigate some related properties. We describe the union of elements of this class. Using the intersection of all special subsets connected with a subset, we give a necessary and sufficient condition for a subset to be a filter.  Finally, by defining some operations, we endow this class with a residuated lattice structure and prove that it is isomorphic to the set of all congruence classes with respect to a filter. %U https://jart.guilan.ac.ir/article_3687_5299c0b4ef0a8acd5f965ad25c45b012.pdf