Abstract
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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.
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Keywords
Krull–Schmidt property, Matlis duality, Matlis reflexive
module, pure-injective module
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Mathematical Subject Classification
Primary: 13C60
Secondary: 13E05, 16D70
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Milestones
Received: 30 April 2024
Revised: 18 February 2025
Accepted: 10 May 2025
Published: 3 June 2025
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| © 2025 The Author(s), under
exclusive license to MSP (Mathematical Sciences Publishers).
Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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