Noetherian properties of rings of differential operators of affine semigroup algebras

Details Noetherian properties of rings of differential operators of affine semigroup algebras Noetherian properties of rings of differential operators of affine semigroup algebras

2007-01-19

arxiv.org/abs/math/0701529v1

Mathematics

Rings and Algebras

21 pages

Scientific paper

We consider the Noetherian properties of the ring of differential operators of an affine semigroup algebra. First we show that it is always right Noetherian. Next we give a condition, based on the data of the difference between the semigroup and its scored closure, for the ring of differential operators being anti-isomorphic to another ring of differential operators. Using this, we prove that the ring of differential operators is left Noetherian if the condition is satisfied. Moreover we give some other conditions for the ring of differential operators being left Noetherian. Finally we conjecture necessary and sufficient conditions for the ring of differential operators being left Noetherian.

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