On Matlis reflexive modules
arXiv:2404.16711 · doi:10.2140/pjm.2025.337.257
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.
12 pages. Minor changes. Final version accepted for publication with Pacific Journal of Mathematics