# Generating degrees for graded projective resolutions

## TL;DR

This paper develops a framework linking theories on the linearity of graded modules, focusing on tensor products of graded bimodules and providing a tool to evaluate degrees in graded projective resolutions.

## Contribution

It introduces a new framework connecting existing theories and offers a method to determine degrees in projective resolutions based on initial generating degrees.

## Key findings

- Established a connection between theories of linearity in graded modules.
- Provided a tool to evaluate degrees in projective resolutions.
- Enhanced understanding of tensor products of graded bimodules.

## Abstract

We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras. Finally, we provide a tool to evaluate the possible degrees of a module appearing in a graded projective resolution once the generating degrees for the first term of some particular projective resolution are known.