$\Sigma $-pure injectivity and Brown representability

DOI10.1090/S0002-9939-2015-12481-1zbMath1371.16006arXiv1304.0979OpenAlexW2908279850WikidataQ122467197 ScholiaQ122467197MaRDI QIDQ5246905

Simion Sorin Breaz

Publication date: 22 April 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.0979

zbMATH Keywords

Brown representability theorempure-semisimple ring\(\Sigma\)-pure injectivity

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Module categories in associative algebras (16D90) Chain complexes (category-theoretic aspects), dg categories (18G35)

Related Items

The dual of Brown representability for some derived categories ⋮ Constructing cogenerators in triangulated categories and Brown representability

Cites Work

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• The dual of Brown representability for some derived categories
• Locally well generated homotopy categories of complexes
• Copure-injective modules
• Brown representability for the dual
• The dual of Brown representability for homotopy categories of complexes
• Pure theories
• Purity, algebraic compactness, direct sum decompositions, and representation type
• Brown representability often fails for homotopy categories of complexes
• Rings whose Right Modules are Direct Sums of Indecomposable Modules
• Localization in Categories of Complexes and Unbounded Resolutions
• Tilting preenvelopes and cotilting precovers

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