Document Type
Original Article
Subject Areas
Mathematics and Statistics
Keywords
MS-algebras, K_2-algebras, GMS-algebras, Modular GMS-algebras, ▁K_2-algebras, Filters, Congruences, Lattice congruences.
Abstract
In this paper, we introduce and characterize the notions of j-filters and principal j-filters of a locally bounded -algebra with . Many properties of j-filters of a locally bounded algebra are investigated, and a set of equivalent conditions for a filter to be a j-filter is given. Also, we show that the class of all j-filters of forms a bounded modular lattice. We obtain many interesting properties of the principal j-filters of a locally bounded -algebra . Moreover, a characterization of a j-filter of a locally bounded -algebra is given in terms of principal j-filters of . We establish and characterize the lattice of all j-lattice congruences of a locally bounded -algebra via j-filters and the lattice of all principal j-lattice congruences via principal j-filters of . Finally, we prove that the principal j-lattice congruence is a -congruence on if and only if is a Boolean element of such that
How to Cite This Article
El-Fawal, Ragaa; Badawy, Abd El-Mohsen; and Hassanein, Abd El-Rahman
(2024)
"j-filters and j-congruences of locally bounded K _2-algebras,"
Al-Azhar Bulletin of Science: Vol. 35:
Iss.
3, Article 6.
DOI: https://doi.org/10.58675/2636-3305.1688