Kolluru VenkateswarluMekonnen Mamo2025-08-172025-08-172024-08https://etd.aau.edu.et/handle/123456789/6941In 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.en-USFurther Moretheory of BH-LatticesThesis