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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the endofiniteness of a key module over pure semisimple rings

Author(s): Nguyen Viet Dung; José Luis García
Journal: Proc. Amer. Math. Soc. 138 (2010), 2269-2278.
MSC (2010): Primary 16G10; Secondary 16D70, 16D90
Posted: February 23, 2010
MathSciNet review: 2607855
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Let be a left pure semisimple ring such that there are no non-zero homomorphisms from preinjective modules to non-preinjective indecomposable modules in -mod, and let be the left key -module; i.e., is the direct sum of all non-isomorphic non-preinjective indecomposable direct summands of products of preinjective left -modules. We show that if the module is endofinite, then is a ring of finite representation type. This settles a question considered in [L. Angeleri Hügel, A key module over pure-semisimple hereditary rings, J. Algebra 307 (2007), 361-376] for hereditary rings.

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