In this paper, we considered the theory of quasideterminants and row and
column determinants. We considered the application of this theory to the
solving of a system of linear equations in quaternion algebra. We established
correspondence between row and column determinants and quasideterminants of
matrix over quaternion algebra.

In the paper I considered definition and structure of linear mapping of
Banach algebra over commutative ring. Based on this definition I explore
derivative of continuous mapping.

Theory of representations of F-algebra is a natural development of the theory
of F-algebra. Morphism of the representation is the map that conserve the
structure of the representation. Exploring of morphisms of the representation
leads to the concepts of generating set and basis of representation. In the
book I considered the notion of tower of representations of F_i-algebras, i=1
>..., n, as the set of coordinated representations of F_i-algebras.

In this paper I explore the set of quaternion algebras over field. In
contrast to quaternion algebra H=E(R,-1,-1), linear function of quaternion
algebra E(C,-1,-1) over complex field satisfies to the Cauchy--Riemann
equations.