✦ LIBER ✦

Extending modules with injective or semisimple summands

✍ Scribed by Catarina Santa-Clara

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 785 KB
Volume: 127
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(96)00156-9

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✦ Synopsis

We characterize when the direct sum of an extending module and an injective module is extending and when the direct sum of an extending module with the finite exchange property and a semisimple module is extending. We also characterize when the direct sum of a uniformextending module and a semisimple module is uniform-extending and, in consequence, we prove that, for a right Noetherian ring R, an extending right R-module Mt and a semisimple right R-module Mz, the right R-module MI @Mz is extending if and only if Mz is Mt/Soc(Mr )injective.