Isomorphism theorems for crossed squares of non-commutative associative algebras and their morphisms

This study consists of five parts. In the first chapter, information about the literature on crossed squares of algebras is presented. In the second chapter, basic algebraic concepts and theorems are given. In the third chapter, crossed modules of algebras are discussed in detail, concepts such as subcrossed module, ideal, kernel and image of crossed module homomorphism, quotient crossed module are defined, and proofs of isomorphism theorems for crossed modules of algebras are given. In the fourth chapter, the concepts given in the previous chapter are adapted for the crossed squares of algebras and it is proved that the isomorphism theorems are still valid under the new definitions given. In the last chapter, the results obtained in the previous chapters are interpreted. Keywords: Algebra, crossed module, isomorphism theorems, crossed square