engleski

Artin-Rees property and Artin-Rees rings

We study the problem of which ideals in Noetherian rings have the Artin-Rees property, and want to obtain new deals with this property from those for which we know that stisfy it. We show that the class AR-Ring_c, of all (Noetherian) Artn-Rees rings in which every prime ideal is moreover completely prime, is closed under localization at arbitrary denominator set. We discuss and illustrate our reults on two particular examples: the enveloping algebra of sl(2) and the tree-dimensional Heisenberg Lie algebra.

Noetherian ring ; Artin-Rees property ; Artin-Rees ring ; prime ideal ; completely prime ideal ; localization ; universal enveloping algebra

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