Further More on the theory of BH-Lattices
| dc.contributor.advisor | Kolluru Venkateswarlu | |
| dc.contributor.author | Mekonnen Mamo | |
| dc.date.accessioned | 2025-08-17T23:16:39Z | |
| dc.date.available | 2025-08-17T23:16:39Z | |
| dc.date.issued | 2024-08 | |
| dc.description.abstract | In this dissertation, we study further properties of BH-lattices, which is a subclass of BH-monoids. We furnish certain examples of BH-monoids that are not BH-lattices. We give a characterization of BH-lattice in terms of bounded BH-lattice and commutative l-group. Also, we prove that every BH-lattice is a direct product of Heyting algebra and commutative l-group under certain conditions. Further, we obtain the decomposition theorem in terms of Boolean algebra and a commutative l-group. Moreover, we introduce the concept of filters in BH-lattices and furnish certain examples. We obtain certain basic properties of BH-lattices. Also, we characterize the filter generated by a given subset of a BH-lattice. Besides these, we prove that the set of all filters with set inclusion forms a Heyting algebra Furthermore, we define the congruence relation on BH-lattices and obtain a one-toone correspondence between the set of congruences and the filter of BH-lattices, which gives more insight for constructing quotient algebra. Also, we prove that the quotient algebra is a BH-lattice. Finally, we introduce different types of filters in BH-lattices, furnish examples, and prove certain properties of each type of filter, their interrelation, and state some open problems for further study in the area. | |
| dc.identifier.uri | https://etd.aau.edu.et/handle/123456789/6941 | |
| dc.language.iso | en_US | |
| dc.publisher | Addis Ababa University | |
| dc.subject | Further More | |
| dc.subject | theory of BH-Lattices | |
| dc.title | Further More on the theory of BH-Lattices | |
| dc.type | Thesis |