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On the Class of Subsets of Residuated lattice which induces a Congruence Relation | ||
| Journal of Algebra and Related Topics | ||
| مقاله 1، دوره 7، شماره 1، شهریور 2019، صفحه 1-12 اصل مقاله (267.99 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2019.11333.1119 | ||
| نویسنده | ||
| H. Harizavi* | ||
| Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Residuated lattice؛ Filter؛ Complement-closed؛ Congruence Relation | ||
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آمار تعداد مشاهده مقاله: 802 تعداد دریافت فایل اصل مقاله: 958 |
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