LINK CLOSED SETS OF PRIME IDEALS AND STABILITY ON BIMODULES

Year 2015, Volume: 17 Issue: 17, 188 - 198, 01.06.2015

Karl A. Kosler

https://doi.org/10.24330/ieja.266220

Abstract

Over a Noetherian ring R, each of a weakly symmetric pair of
torsion radicals is shown to be stable on Noetherian R-R bimodules if and
only if the set of prime ideals that are closed with respect to each torsion
radical is closed under links. Such a pair for R, termed a weakly symmetric
stable pair, is extended to a weakly symmetric stable pair for any Noetherian
extension ring of R. In case classical Krull dimension is a link invariant, we
give a positive answer to the incomparability question for linked prime ideals
in certain extension rings of R.

Keywords

Noetherian ring, extension ring, prime ideal, link, torsion radical, classical Krull dimension