自由代数的线性映射
Linear Mappings of Free Algebra
摘要：
对于定义了加法运算的任意F-代数，研究了映射矩阵的生环问题。矩阵的和由F-代数中的和决定，矩阵的乘积由映射的乘积决定。矩阵为映射矩阵的方程组称为加法方程组。考虑了可加性方程组的求解方法。作为一个例子，我考虑复域上一个线性方程组的解，只要方程中含有未知量及其共轭。交换环上代数的线性映射保持代数的加法运算和代数的元素与环的元素的乘积。张量积A \otimes A在代数A中的表示生成代数A的线性变换的集合。这一研究结果将对处理不同代数的数学家和物理学家有用。
英文摘要：
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.
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