Resolving decompositions for polynomial modules (Q1634505)

In the paper under review, the authors introduce the novel concept of a resolving decomposition of a polynomial module as a combinatorial structure that allows for the effective construction of free resolutions. It provides a unifying framework for recent results of the authors for different types of bases. This article represents a revised and expanded version of [\textit{M. Albert} and \textit{W. M. Seiler}, Lect. Notes Comput. Sci. 9890, 15--29 (2016; Zbl 1453.13039)] which was presented at the conference ``Computer Algebra in Scientific Computing''.