One-Sided Operators in Rings (UMAP)

This module provides concrete examples (n x n matrices with n greater than or equal to 4) of one-sided identities and both one-sided and two-sided annihilators, seemingly bizarre phenomena that can occur in non-commutative rings. Students construct rings of low-dimensional matrices that contain left-only, right-only, and non-zero two-sided annihilators.

Table of Contents:

1. MOTIVATION

2. PRELIMINARIES

3. THE SIMPLEST EXAMPLE

4. IDEALS AND RESIDUE CLASSES

5. EXAMPLES OF SPECIAL RINGS

6. EXERCISES

7. REFERENCE

8. SELF-STUDY QUIZ

9. SOLUTIONS TO THE EXERCISES

10. ANSWERS TO THE SELF-STUDY QUIZ