In this paper, the notion of cyclic B-algebras is introduced and some of its properties are investigated. Also, the laws of exponents for Balgebras are determined. Lastly, this paper seeks to confirm whether the class of cyclic B-algebras and the class of cyclic groups coincide.
In this study, we investigate the topology on B-algebras: an algebraic system of propositional logic. We define here the notion of topological B-algebras (briefly, TB-algebras) and some properties are investigated. A characterization of TB-algebras based on neighborhoods is provided. We also provide a filterbase that generates a unique B-topology, making a TB-algebra in which the filterbase is a neighborhood base of the constant element, provided that the given B-algebra is commutative. Finally, we investigate subalgebras of TB-algebras and introduce the notion of quotient TB-algebras of the given B-algebra.
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