LINK CLOSED SETS OF PRIME IDEALS AND STABILITY ON BIMODULES

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International Electronic Journal of Algebra
Volume:17 Issue:17
LINK CLOSED SETS OF PRIME IDEALS AND STABILITY ON BIMODULES

LINK CLOSED SETS OF PRIME IDEALS AND STABILITY ON BIMODULES

Pages : 188-198

View : 14 | Download : 13

Publication Date : 2015-06-01

Article Type : Research Paper

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

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