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.
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