  I dedicated the volume $1$ of monograph 'Introduction into Noncommutative
Algebra' to studying of algebra over commutative ring. The main topics that I
covered in this volume: definition of module and algebra over commutative ring;
linear map of algebra over commutative ring; vector space over associative
division algebra; system of linear equations over associative division algebra;
homomorphism of vector space over associative division algebra and covariance
theory; eigenvalue and eigenvector over associative division algebra.
