English

The realization problem for von Neumann regular rings

Rings and Algebras 2015-03-23 v2

Abstract

We survey recent progress on the realization problem for von Neumann regular rings, which asks whether every countable conical refinement monoid can be realized as the monoid of isoclasses of finitely generated projective right RR-modules over a von Neumann regular ring RR.

Keywords

Cite

@article{arxiv.0802.1872,
  title  = {The realization problem for von Neumann regular rings},
  author = {Pere Ara},
  journal= {arXiv preprint arXiv:0802.1872},
  year   = {2015}
}

Comments

15 pages, survey paper. It contains a new version of Proposition 4.1, due to Ken Goodearl

R2 v1 2026-06-21T10:12:19.913Z