j-filters and j-congruences of locally bounded K _2-algebras | ||
| Al-Azhar Bulletin of Science | ||
| Volume 2024, Issue 1, January 2024 | ||
| DOI: 10.58675/2636-3305.1688 | ||
| Authors | ||
| Ragaa El-Fawal1; Abd El-Mohsen Badawy2; Abd El-Rahman Hassanein3 | ||
| 1Department of Mathematics Faculty of Science (girls branch), El-Azhar University, Egypt | ||
| 2Department of Mathematics Faculty of Science, Tanta University, Egypt | ||
| 3Department of Mathematics Faculty of Science, El-Azhar University, Egypt | ||
| 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 | ||
| Keywords | ||
| MS-algebras; K_2-algebras; GMS-algebras; Modular GMS-algebras; ▁K_2-algebras; Filters; Congruences; Lattice congruences | ||
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