On the Class of Subsets of Residuated lattice which induces a Congruence Relation
Publish place: The Journal of Algebra and Related Topics، Vol: 7، Issue: 1
Publish Year: 1398
Type: Journal paper
Language: English
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Document National Code:
JR_JART-7-1_001
Index date: 21 July 2024
On the Class of Subsets of Residuated lattice which induces a Congruence Relation abstract
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.
On the Class of Subsets of Residuated lattice which induces a Congruence Relation Keywords:
On the Class of Subsets of Residuated lattice which induces a Congruence Relation authors
H. Harizavi
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
