# Generalized local ring

## Contents

## Definition

### Symbol-free definition

A positively graded commutative unital ring *R* is termed a **generalized local ring** if its degree 0 part is local and Noetherian, and *R* is a finitely generated as an algebra over its degree 0 part.

## Metaproperties

### Uniqueness of maximal ideal

A generalized local ring has a unique maximal homogeneous ideal.