Reducibility of parameter ideals in low powers of the maximal ideal
Peer reviewed, Journal article
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Date
2021Metadata
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- Institutt for matematiske fag [2354]
- Publikasjoner fra CRIStin - NTNU [37247]
Original version
10.1090/conm/773Abstract
A commutative noetherian local ring (R, m) is Gorenstein if and only if every parameter ideal of R is irreducible. Although irreducible parameter ideals may exist in non-Gorenstein rings, Marley, Rogers, and Sakurai show there exists an integer ` (depending on R) such that R is Gorenstein if and only if there exists an irreducible parameter ideal contained in m` . We give upper bounds for ` that depend primarily on the existence of certain systems of parameters in low powers of the maximal ideal.