Simplifying Smoktunowicz's Extraordinary Example

Abstract

At the turn of the 21st century Agata Smoktunowicz constructed the first example of a nil algebra over a countable field such that the polynomial ring over the algebra is not nil. This answered an old question of Amitsur. We present a simplification of the example.

Key Words:

• Jacobson radical
• Nil ring
• Polynomial ring

2010 Mathematics Subject Classification:

• Primary 16N40
• Secondary 16N20, 16S36

ACKNOWLEDGMENT

I wish to thank Agata Smoktunowicz for encouraging me to make this work public, Victor Camillo for the countless hours of reading manuscripts and talking about simplifications, and George Bergman for some extensive and much appreciated suggestions.

Notes

Communicated by A. Smoktunowicz.