A more common way to describe a Euclidean ring.
Euclidean Domain
See also
Algebraic Number Theory, Euclidean RingThis entry contributed by Todd Rowland
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Rowland, Todd. "Euclidean Domain." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/EuclideanDomain.html