Definition: A domain which has a Euclidean valuation

- N. Jacobson. Basic algebra I. (2012) @ Section 2.16

- passes to localizations

- passes to quotient rings (Counterexample: $R_{ 49 }$ is a homomorphic image of $R_{ 27 }$)
- passes to subrings (Counterexample: $R_{ 6 }$ is a subring of $R_{ 101 }$)
- stable under finite products (Counterexample: $R_{ 9 }$)
- stable under products (counterexample needed)
- forms an equational class (counterexample needed)

Rings

Legend

- = has the property
- = does not have the property
- = information not in database