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 $\ARRingc$, 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
Datum izdavanja:
8.12.2010.
Posjeta: 1.681 *