# The graded structure of algebraic Cuntz-Pimsner rings

## TL;DR

This paper classifies various graded structures of algebraic Cuntz-Pimsner rings and characterizes certain fractional skew monoid rings using corner automorphisms, advancing understanding of their algebraic properties.

## Contribution

It provides a classification of strongly, epsilon-strongly, and nearly epsilon-strongly graded algebraic Cuntz-Pimsner rings and characterizes noetherian and artinian fractional skew monoid rings.

## Key findings

- Classification of graded Cuntz-Pimsner rings up to isomorphism
- Characterization of noetherian fractional skew monoid rings
- Characterization of artinian fractional skew monoid rings

## Abstract

The algebraic Cuntz-Pimsner rings are naturally $\mathbb{Z}$-graded rings that generalize both Leavitt path algebras and unperforated $\mathbb{Z}$-graded Steinberg algebras. We classify strongly, epsilon-strongly and nearly epsilon-strongly graded algebraic Cuntz-Pimsner rings up to graded isomorphism. As an application, we characterize noetherian and artinian fractional skew monoid rings by a single corner automorphism.