Izvorni znanstveni članak

Artin-Rees property and Artin-Rees rings

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

Sažetak

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 $\text{ARRingc}$, 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.

Ključne riječi

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

Datum izdavanja:

8.12.2010.

Posjeta: 1.881 *