Artin-Rees property and Artin-Rees rings

作者：Sirola Boris^*

来源：Mathematical Communications, 2010, 15(2): 479-488.

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

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

• 出版日期2010-12