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.
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