Definition: A commutative division ring

- N. Jacobson. Basic algebra II. (2012) @ Parts 8+11

- passes to $eRe$ for any full idempotent $e$
- passes to localizations
- passes to the center

- Morita invariant (counterexample)
- passes to $eRe$ for any idempotent $e$ (counterexample needed)
- passes to matrix rings (counterexample)
- passes to polynomial rings (counterexample)
- passes to power series ring (counterexample)
- passes to subrings (counterexample)
- stable under finite products (counterexample)
- stable under products (counterexample)