English

Affine Noetherian algebras, filtrations and presentations

Rings and Algebras 2022-11-03 v1

Abstract

Resco and Small gave the first example of an affine Noetherian algebra which is not finitely presented. It is shown that their algebra has no finite-dimensional filtrations whose associated graded algebras are Noetherian, affirming their prediction. A modification of their example yields countable fields over which `almost all' (that is, a co-countable continuum of) affine Noetherian algebras lack such a filtration, and an answer to a question suggested by Irving and Small is derived.

Keywords

Cite

@article{arxiv.2211.00935,
  title  = {Affine Noetherian algebras, filtrations and presentations},
  author = {Be'eri Greenfeld},
  journal= {arXiv preprint arXiv:2211.00935},
  year   = {2022}
}

Comments

Accepted for publication in Proc. Amer. Math. Soc

R2 v1 2026-06-28T04:59:26.745Z