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Indecomposable Decompositions of Pure-Injective Objects and the Pure-Semisimplicity

✍ Scribed by Pedro A Guil Asensio; Daniel Simson

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
117 KB
Volume
244
Category
Article
ISSN
0021-8693

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✦ Synopsis

dedicated to rüdiger göbel on the occasion of his 60th birthday

We give a criterion for the existence of an indecomposable decomposition of pure-injective objects in a locally finitely presented Grothendieck category (Theorem 2.5). As a consequence we get Theorem 3.2, asserting that an associative unitary ring R is right pure-semisimple if and only if every right R-module is a direct sum of modules that are pure-injective or countably generated. Some open problems are formulated in the paper.

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