English

On Matlis reflexive modules

Commutative Algebra 2025-06-04 v3 Representation Theory

Abstract

Matlis duality for modules over commutative rings gives rise to the notion of Matlis reflexivity. It is shown that Matlis reflexive modules form a Krull-Schmidt category. For noetherian rings the absence of infinite direct sums is a characteristic feature of Matlis reflexivity. This leads to a discussion of objects that are extensions of artinian by noetherian objects. Classifications of Matlis reflexive modules are provided for some small examples.

Keywords

Cite

@article{arxiv.2404.16711,
  title  = {On Matlis reflexive modules},
  author = {Henning Krause},
  journal= {arXiv preprint arXiv:2404.16711},
  year   = {2025}
}

Comments

12 pages. Minor changes. Final version accepted for publication with Pacific Journal of Mathematics

R2 v1 2026-06-28T16:06:31.641Z