Endomorphism rings of completely pure-injective modules |
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Authors: | José L Gó mez Pardo Pedro A Guil Asensio |
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Institution: | Departamento de Alxebra, Universidade de Santiago, 15771 Santiago de Compostela, Spain ; Departamento de Matematicas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain |
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Abstract: | Let be a ring, its injective envelope, and the Jacobson radical of . It is shown that if every finitely generated submodule of embeds in a finitely presented module of projective dimension , then every finitley generated right -module is canonically isomorphic to . This fact, together with a well-known theorem of Osofsky, allows us to prove that if, moreover, is completely pure-injective (a property that holds, for example, when the right pure global dimension of is and hence when is a countable ring), then is semiperfect and is finite-dimensional. We obtain several applications and a characterization of right hereditary right noetherian rings. |
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Keywords: | |
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