# Uniserial Noetherian Centrally Essential Rings

## TL;DR

This paper characterizes right uniserial, right Noetherian centrally essential rings, showing they are either commutative discrete valuation domains or certain Artinian rings, and demonstrates the existence of non-commutative examples.

## Contribution

It provides a complete characterization of right uniserial, right Noetherian centrally essential rings and proves the existence of non-commutative uniserial Artinian centrally essential rings.

## Key findings

- Characterization of rings as either commutative discrete valuation domains or Artinian rings
- Existence of non-commutative uniserial Artinian centrally essential rings
- Complete classification of right uniserial, right Noetherian centrally essential rings

## Abstract

It is proved that a ring $R$ is a right uniserial, right Noetherian centrally essential ring if and only if $R$ is a commutative discrete valuation domain or a left and right Artinian, left and right uniserial ring. It is also proved that there exist non-commutative uniserial Artinian centrally essential rings. Victor Markov is supported by the Russian Foundation for Basic Research, project 17-01-00895-A. Askar Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013.