Solvable Differential Graded R-Modules Algorithms (SDGMA): A Mathematical Approach

Abstract

This article describes the Solvable Differential Graded R-Modules Algorithms (SDGMA) package, a GAP package to construct a classification for some types of differential graded R-modules. Due to the great importance of graduation of rings and modules, the study of this concept attracted wide interest from mathematicians everywhere. We have constructed a classification for some types of differential graded R-modules. This classification gives a partial algorithm to test whether such modules are solvable. For modules outside the classification, we cannot decide, using our methods, whether or not they are solvable. This classification depends on two basic factors; the dimension D of the module and the degree of the differential on the module P. These two factors are the input for the main function SolvableModule in our algorithm. In addition, if the module is solvable then the package gives the proof that it is solvable. For modules outside the classification, we cannot decide, using our methods, whether or not they are solvable.