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Decomposition of injective modules relative to a torsion theory

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Abstract

IfR is a right noetherian ring, the decomposition of an injective module, as a direct sum of uniform submodules, is well known. Also, this property characterises this kind of ring. M. L. Teply obtains this result for torsion-free injective modules. The decomposition of injective modules relative to a torsion theory has been studied by S. Mohamed, S. Singh, K. Masaike and T. Horigone. In this paper our aim is to determine those rings satisfying that every torsion-freeτ-injective module is a direct sum ofτ-uniformτ-injective submodules and also to determine those rings with the same property for everyτ-injective module.

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Authors and Affiliations

  1. Departmento de Algebra y Fundamentos, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    José L. Bueso, Pascual Jara & Blas Torrecillas

Authors
  1. José L. Bueso
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  2. Pascual Jara
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  3. Blas Torrecillas
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Bueso, J.L., Jara, P. & Torrecillas, B. Decomposition of injective modules relative to a torsion theory. Israel J. Math. 52, 266–272 (1985). https://doi.org/10.1007/BF02786522

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  • DOI: https://doi.org/10.1007/BF02786522

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