On the importance of being primitive

TL;DR

This paper surveys the concept of primitivity in ring theory, focusing on characterizations of primitive ideals across different classes of rings, highlighting their significance in understanding ring structures.

Contribution

It provides a comprehensive overview of primitive ideals and their characterizations in various classes of rings, clarifying their role in ring theory.

Findings

Summarizes key characterizations of primitive ideals.

Highlights differences across ring classes.

Provides insights into the structure of primitive ideals.

Abstract

We give a brief survey of primitivity in ring theory and in particular look at characterizations of primitive ideals in the prime spectrum for various classes of rings.