[FOM] Transfinite Euclidean Algorithm

joeshipman@aol.com joeshipman at aol.com
Mon Nov 12 15:35:21 EST 2007

Commutative rings exist in which there is no Euclidean algorthm, but 
there is a "division algorithm" in which the appropriate "norm" with 
respect to which the remainder decreases takes values in a more complex 
well-ordered set than the integers. Can anyone give a simple example of 
such a ring?

-- JS
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