Narrow Results

The following sections are included:

• Introduction
• Polya’s Recurrence Theorem
• Burnside’s Problem
• Conclusion
• Bibliography

We look at structure results in nearring theory, especially with regard to Jacobson style primitivity. We look at some applications in state automata and cellular automata, where we find interesting structures. We then look at generalising planarity and nearfields, some of the best structured nearrings, and find that Jacobson style primitivity plays an important role.

The paper explores some of our recent work and presents several ways forward that we think might be of value. While we hope to answer some of the questions that we raise here, it is likely that other researchers will find simpler ways forward that we are unable to see. We look forward to some surprises!