Isomorphism theorems for crossed squares of algebras and their morphisms

This thesis consists of five chapters. In the first chapter, information and literature researches about the subject studied and the aim of the thesis are given. In the second chapter, some basic concepts and propositions used in algebra are given. In the third chapter, crossed module is defined and the notion of a crossed module in commutative algebras is discussed in detail, and subcrossed modules of crossed modules of commutative algebras, ideals of crossed modules and kernel and image of crossed module morphism are introduced. Also, important isomorphism theorems of crossed modules of commutative algebras have been proved. In the fourth chapter, using the definition of crossed squares of commutative algebras, among the necessary elements of the structure, the subcrossed square, the ideal of crossed squares and the kernel and image of crossed square morphisms are introduced. In the continuation of this chapter, the first, second and third isomorphism theorems are proved in crossed squares of commutative algebras. In the fifth and last chapter, the contributions to the literature and the results are given in the light of the obtainments.