Preinjective modules over pure semisimple rings |
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Authors: | Nguyen Viet Dung José Luis García |
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Institution: | a Department of Mathematics, Ohio University-Zanesville, Zanesville, OH 43701, USA b Department of Mathematics, University of Murcia, 30071 Murcia, Spain |
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Abstract: | For a left pure semisimple ring R, it is shown that the local duality establishes a bijection between the preinjective left R-modules and the preprojective right R-modules, and any preinjective left R-module is the source of a left almost split morphism. Moreover, if there are no nonzero homomorphisms from preinjective modules to non-preinjective indecomposable modules in R-mod, the direct sum of all non-preinjective indecomposable direct summands of products of preinjective left R-modules is a finitely generated product-complete module. This generalizes a recent theorem of Angeleri Hügel L. Angeleri Hügel, A key module over pure-semisimple hereditary rings, J. Algebra 307 (2007) 361-376] for hereditary rings. |
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Keywords: | 16G10 16D70 16D90 |
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