[FOM] Transfinite Euclidean Algorithm

[hendrik@topoi.pooq.com]

On Mon, Nov 12, 2007 at 03:35:21PM -0500, joeshipman at aol.com wrote:
> 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

polynomials over the integers with ordinal exponents but only a 
finite number of terms in each polynomial?

Or have I misunderstood the question?

-- hendrik