Reducibility of parameter ideals in low powers of the maximal ideal
Peer reviewed, Journal article
Published version
Åpne
Permanent lenke
https://hdl.handle.net/11250/2991503Utgivelsesdato
2021Metadata
Vis full innførselSamlinger
- Institutt for matematiske fag [2350]
- Publikasjoner fra CRIStin - NTNU [37177]
Originalversjon
10.1090/conm/773Sammendrag
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.