Hi Nils,
On 2015-02-19, Nils Bruin <[email protected]> wrote:
> Doesn't the second (local) ordering violate the "usual" part? You would
> have 1>x>x^2>... etc., which is not allowed according to, for instance, the
> definition in [Section 15.2 in Eisenbud, Commutative Algebra with a view
> towards Algebraic Geometry, GTM 150, Springer 2004]]
Have a look at the book of Greuel, Pfister et al ("A Singular
introduction to commutative algebra"). Local orderings of course have
the problem that reductions may not be as easily to handle (think of the
relation x=x^2 with x^2<x and try to compute the normal forma of x with
respect to that relation). But if you compute so-called *weak* normal
forms in a localisation (i.e. 1-x is a unit), then local orderings are a
good tool.
Best regards,
Simon
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