The Cohen–macaulay Property of Invariant Rings Over the Integers

Almuhaimeed, Areej

doi:10.1007/s00031-020-09612-1

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2022

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“…The main result of this article is a generalization of Broers result to the situation where the field K is replaced by an arbitrary Noetherian integral domain. Some results regarding the question when rings of invariants over Z are Cohen-Macaulay rings can be found in [1].…”

Section: Introductionmentioning

confidence: 99%

A degree bound for rings of arithmetic invariants

David¹

2022

Preprint

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Consider a Noetherian domain R and a finite group G ⊆ Gl n (R). We prove that if the ring of invariants R[x 1 , . . . , x n ] G is a Cohen-Macaulay ring, then it is generated as an R-algebra by elements of degree at most max(|G|, n(|G| − 1)). As an intermediate result we also show that if R is a Noetherian local ring with infinite residue field then such a ring of invariants of a finite group G over R contains a homogeneous system of parameters consisting of elements of degree at most |G|.

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Section: Introductionmentioning

confidence: 99%

A degree bound for rings of arithmetic invariants

David¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

The Cohen–macaulay Property of Invariant Rings Over the Integers

Cited by 1 publication

References 16 publications

A degree bound for rings of arithmetic invariants

A degree bound for rings of arithmetic invariants

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