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Indecomposable decompositions of completely pure-injective modules

Catarina Araújo de Santa-Clara Gomes
Venezia 2002 (Algebra Conference), Island of San Servolo, Italy

We characterize when a countably generated pure-injective module is a direct sum of indecomposable direct summands in terms of its pure quotients. Under certain additional hypotheses, our characterization can be extended to non-countable modules. This result completes previous characterizations given by J.L. Gomez Pardo, P.A. Guil and D. Simson. Joint work with A.P. Alexandre and P. A. Guil. Primary 16S50. Secondary: 16D50, 16E60.