paper

Linear Mappings of Free Algebra

arXiv:1003.1544

Abstract

For arbitrary F-algebra, in which the operation of addition is defined, I explore biring of matrices of mappings. The sum of matrices is determined by the sum in F-algebra, and the product of matrices is determined by the product of mappings. The system of equations, whose matrix is a matrix of mappings, is called a system of additive equations. I considered the methods of solving system of additive equations. As an example, I consider the solution of a system of linear equations over the complex field provided that the equations contain unknown quantities and their conjugates. Linear mappings of algebra over a commutative ring preserve the operation of addition in algebra and the product of elements of the algebra by elements of the ring. The representation of tensor product A\otimes A in algebra A generates the set of linear transformations of algebra A. The results of this research will be useful for mathematicians and physicists who deal with different algebras.

English text - 79 pages; Russian text - 81 pages. Established a link between linear mappings and tensor of order 2. Described the structure of the linear mapping of algebra

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