Modules

Multivariate Dimension Polynomials of Inversive Difference Field Extensions

“…This paper is dedicated to the memory of my dear teacher, Alexander Vasilyevich Mikhalev, who has made profound contributions to several areas of mathematics, especially to various branches of algebra including the ring theory, homological algebra, differential and difference algebra, computer algebra, algebraic K-theory, topological algebra, and coding theory. In his works on differential and difference algebraic structures [5], [6], [28], [18] - [24], [25] - [28] and in some other papers A. V. Mikhalev obtained a number of fundamental results on differential and difference rings and modules, characteristic sets of differential and difference polynomials, and computational analysis of systems of algebraic differential and difference equations. He has also presented excellent expositions of ideas and methods of differential and difference algebra in his books [6], [28] and papers [25] and [27].…”

“…In his works on differential and difference algebraic structures [5], [6], [28], [18] - [24], [25] - [28] and in some other papers A. V. Mikhalev obtained a number of fundamental results on differential and difference rings and modules, characteristic sets of differential and difference polynomials, and computational analysis of systems of algebraic differential and difference equations. He has also presented excellent expositions of ideas and methods of differential and difference algebra in his books [6], [28] and papers [25] and [27]. Of special note is the paper [26] where A. V. Mikhalev and E. V. Pankratiev discovered a very interesting relationship between E. Kolchin's differential dimension polynomials and A. Einstein's concept of strength of a system of algebraic differential equations.…”