Further More on the theory of BH-Lattices
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Date
2024-08
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Addis Ababa University
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.
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Further More, theory of BH-Lattices