Let be a graded ring. We introduce a class of graded -modules called Gröbner-coherent modules. Roughly, these are graded -modules that are coherent as ungraded modules because they admit an adequate theory of Gröbner bases. The class of Gröbner-coherent modules is formally similar to the class of coherent modules: for instance, it is an abelian category closed under extension. However, Gröbner-coherent modules come with tools for effective computation that are not present for coherent modules.
"Gröbner-coherent rings and modules." J. Commut. Algebra 12 (1) 107 - 114, Spring 2020. https://doi.org/10.1216/jca.2020.12.107