Distributive Noetherian Centrally Essential Rings

TL;DR

This paper characterizes right or left Noetherian, distributive centrally essential rings as finite products of either commutative Dedekind domains or uniserial Artinian centrally essential rings, providing a structural classification.

Contribution

It offers a complete structural classification of Noetherian centrally essential rings, identifying their decomposition into specific well-understood components.

Findings

Rings decompose into products of Dedekind domains and uniserial Artinian rings.

Characterization of centrally essential rings in the Noetherian case.

Structural description applicable to both commutative and non-commutative rings.

Abstract

It is proved that a ring $A$ is a right or left Noetherian, right distributive centrally essential ring if and only if $A=A_1\times\cdots\times A_n$, where each of the rings $A_i$ is either a commutative Dedekind domain or a uniserial Artinian centrally essential (not necessarily commutative) ring. V.T.Markov is supported by the Russian Foundation for Basic Research, project 17-01-00895-A. A.A.Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013.