Crossed squares of associative algebras

This thesis consists of eight chapters. In the first chapter, Introduction and goals of thesis are introduced, in the second chapter, literature review,In the third chapter the basic concepts used in the thesis are given. In the next chapter multipliers of an algebra are given and the multiplier algebra is exanimated then the relationship between the multiplication algebra and the action of algebra is discussed. In the next chapter, the non-abelian tensor product of algebras is defined by using compatible actions of the two algebras on each other. Then, the crossed module structure, which is defined using the algebra effect, is examined together with examples. In the sixty chapter, the crossed square of the algebras is examined and by considering the product defined in the fifty chapter, a crossed square is obtained. In the seventy chapter, the relationship between simplicial algebras and the crossed square is discussed. Final chapter conclusion and recommendations is discussed.