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On Centrally Essential Rings

Oleg Lyubimtsev, Askar Tuganbaev

Abstract

A ring $R$ with center $C$ is said to be centrally essential if the module $R_C$ is an essential extension of the module $C_C$. In this paper, we study properties of ideals of centrally essential rings, centrally essential quaternion algebras, and group rings of Hamiltonian groups.

On Centrally Essential Rings

Abstract

A ring with center is said to be centrally essential if the module is an essential extension of the module . In this paper, we study properties of ideals of centrally essential rings, centrally essential quaternion algebras, and group rings of Hamiltonian groups.
Paper Structure (4 sections, 12 equations)

This paper contains 4 sections, 12 equations.

Table of Contents

  1. Introduction
  2. Properties of Right Ideals which Are Semiprime as Rings
  3. Centrally Essential Quaternion Algebras and Group Rings
  4. Supplements and Remarks