English

A note on Non-Noetherian Cohen-Macaulay rings

Commutative Algebra 2019-01-14 v2

Abstract

In this note, we study the Cohen-Macaulayness of non-Noetherian rings. We show that Hochster's celebrated theorem that a finitely generated normal semigroup ring is Cohen-Macaulay does not extend to non-Noetherian rings. We also show that for any valuation domain VV of finite Krull dimension, V[x]V[x] is Cohen-Macaulay in the sense of Hamilton-Marley.

Keywords

Cite

@article{arxiv.1812.05079,
  title  = {A note on Non-Noetherian Cohen-Macaulay rings},
  author = {Youngsu Kim and Andrew Walker},
  journal= {arXiv preprint arXiv:1812.05079},
  year   = {2019}
}

Comments

Fixed typos from the previous version

R2 v1 2026-06-23T06:40:31.358Z