Regularity in residuated lattices
Publish place: Iranian Journal of Fuzzy Systems، Vol: 16، Issue: 6
Publish Year: 1398
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJFS-16-6_010
تاریخ نمایه سازی: 30 خرداد 1400
Abstract:
In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and investigate special residuated lattices in order to obtain new characterizations for the directly indecomposable subvariety of Stonean residuated lattices. Free algebra in varieties of Stonean residuated lattices is constructed. We introduce in residuated lattice a new type of filter called special filter and investigate its properties. Finally, regular filter property in residuated lattices is introduced and is studied in details.
Keywords:
(semi) divisible residuated lattice , Boolean element , directly indecomposable algebra , free algebras
Authors
L. C. Holdon
Faculty of Exact Sciences, Department of Mathematics, University of Craiova, ۱۳, Al. I.Cuza st., ۲۰۰۵۸۵, Craiova, Romania and International Theoretical High School of Informatics Bucharest, ۶۴۸, Colentina st., ۰۲۱۱۸۷ Bucharest, Romania
A. Borumand Saeid
Mahani Mathematical Research center, Shahid Bahonar University of Kerman, Iran, Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran