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Mathematical Communications, Vol. 15 No. 2, 2010.

Original scientific paper

Artin-Rees property and Artin-Rees rings

Boris Širola orcid id orcid.org/0000-0003-1000-0808 ; Department of Mathematics, University of Zagreb, Zagreb, Croatia

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Abstract

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 $\ARRingc$, 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
$\mathfrak{sl}(2)$ and the three-dimensional Heisenberg Lie algebra.

Keywords

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

Hrčak ID:

61874

URI

https://hrcak.srce.hr/61874

Publication date:

8.12.2010.

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