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Mathematics > Commutative Algebra

Title: On Matlis reflexive modules

Authors: Henning Krause
(Submitted on 25 Apr 2024 (v1), last revised 29 Apr 2024 (this version, v2))
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.
Comments: 12 pages. Added further references and a discussion of linearly compact modules
Subjects: Commutative Algebra (math.AC); Representation Theory (math.RT)
MSC classes: 13C60 (primary), 13E05, 16D70 (secondary)
Cite as: arXiv:2404.16711 [math.AC]
  (or arXiv:2404.16711v2 [math.AC] for this version)

Submission history

From: Henning Krause [view email]
[v1] Thu, 25 Apr 2024 16:21:51 GMT (14kb)
[v2] Mon, 29 Apr 2024 06:51:43 GMT (15kb)
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