Compatible ideals in Gorenstein rings

Thomas Polstra; Karl Schwede

Compatible ideals in Gorenstein rings

Commutative Algebra 2022-11-08 v3

Authors: Thomas Polstra , Karl Schwede

Abstract

Suppose $R$ is a $\mathbb{Q}$ -Gorenstein $F$ -finite and $F$ -pure ring of prime characteristic $p>0$ . We show that if $I\subseteq R$ is a compatible ideal (with all $p^{-e}$ -linear maps) then there exists a module finite extension $R\to S$ such that the ideal $I$ is the sum of images of all $R$ -linear maps $S\to R$ .

Keywords

gorenstein rings and modules commutative algebra monomial ideals

Cite

@article{arxiv.2007.13810,
  title  = {Compatible ideals in Gorenstein rings},
  author = {Thomas Polstra and Karl Schwede},
  journal= {arXiv preprint arXiv:2007.13810},
  year   = {2022}
}

Comments

Previous versions of the article proved the main theorem under the additional assumption that the $\mathbb{Q}$-Gorenstein index was relatively prime to the characteristic of $R$. Edits to the proof of the main theorem have been made

Compatible ideals in Gorenstein rings

Abstract

Keywords

Cite

Comments

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