Gröbner-coherent rings and modules

Abstract

Let R be a graded ring. We introduce a class of graded R -modules called Grobner-coherent modules. Roughly, these are graded R -modules that are coherent as ungraded modules because they admit an adequate theory of Grobner bases. The class of Grobner-coherent modules is formally similar to the class of coherent modules: for instance, it is an abelian category closed under extension. However, Grobner-coherent modules come with tools for effective computation that are not present for coherent modules.