On basi̇c algebras and logics

This thesis consists of seven chapters. In the first chapter , the topic of thesis was introduced and preliminary information about the studies which is related to the topic of thesis was given. In the second chapter, some basic concepts was presented to ease readability of thesis. In the third chapter, basic definitions and concepts which are belong to basic algebra was given and it was referred about relation with lattice. Also, indepence of axiom systems of basic algebra was shown and axiom systems which are equal to this axiom systems in different signatures was defined. In the fourth chapter, definitions which are belong to orthomodular lattices and MV-algebras was given and it was referred about relation with basic algebras. In the fifth chapter, definitions of congruence and filter of basic algebras was given. In the sixth chapter, the concept of implication basic algebra and its some properties were given and independence of axioms was proved. In the seventh chapter, it was proved that any interval of a basic algebra is a basic algebra. In the eighth chapter, the solutions of Yang-Baxter equations in basic algebras were mentioned.