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.
Harizavi, H. (2019). On the Class of Subsets of Residuated lattice which induces a Congruence Relation. Journal of Algebra and Related Topics, 7(1), 1-12. doi: 10.22124/jart.2019.11333.1119
MLA
H. Harizavi. "On the Class of Subsets of Residuated lattice which induces a Congruence Relation". Journal of Algebra and Related Topics, 7, 1, 2019, 1-12. doi: 10.22124/jart.2019.11333.1119
HARVARD
Harizavi, H. (2019). 'On the Class of Subsets of Residuated lattice which induces a Congruence Relation', Journal of Algebra and Related Topics, 7(1), pp. 1-12. doi: 10.22124/jart.2019.11333.1119
VANCOUVER
Harizavi, H. On the Class of Subsets of Residuated lattice which induces a Congruence Relation. Journal of Algebra and Related Topics, 2019; 7(1): 1-12. doi: 10.22124/jart.2019.11333.1119
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