When cotorsion modules are pure injective

Journal of Mathematical Logic 9 (1):63-102 (2009)
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We characterize rings over which every cotorsion module is pure injective in terms of certain descending chain conditions and the Ziegler spectrum, which renders the classes of von Neumann regular rings and of pure semisimple rings as two possible extremes. As preparation, descriptions of pure projective and Mittag–Leffler preenvelopes with respect to so-called definable subcategories and of pure generation for such are derived, which may be of interest on their own. Infinitary axiomatizations lead to coherence results previously known for the special case of flat modules. Along with pseudoflat modules we introduce quasiflat modules, which arise naturally in the model-theoretic and the category-theoretic contexts.



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Some Stable Non-Elementary Classes of Modules.Marcos Mazari-Armida - 2023 - Journal of Symbolic Logic 88 (1):93-117.

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References found in this work

Model theory of modules.Martin Ziegler - 1984 - Annals of Pure and Applied Logic 26 (2):149-213.
Remarks on elementary duality.Mike Prest - 1993 - Annals of Pure and Applied Logic 62 (2):183-205.
Purity, Spectra and Localisation.Mike Prest - 2009 - Cambridge University Press.

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