Mermut, E., Santaclara, C. and Smith, P.
(2009)
Injectivity relative to closed submodules.
*Journal of Algebra*, 321(2),
pp. 548-557.
(doi: 10.1016/j.jalgebra.2008.11.004)

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Publisher's URL: http://dx.doi.org/10.1016/j.jalgebra.2008.11.004

## Abstract

Let R be a ring. An R-module X is called c-injective if, for every closed submodule L of every R-module M, every homomorphism from L to X lifts to M. It is proved that if R is a Dedekind domain then an R-module X is c-injective if and only if X is isomorphic to a direct product of homogeneous semisimple R-modules and injective R-modules. It is also proved that a commutative Noetherian domain R is Dedekind if and only if every simple R-module is c-injective.

Item Type: | Articles |
---|---|

Status: | Published |

Refereed: | Yes |

Glasgow Author(s) Enlighten ID: | Smith, Professor Patrick |

Authors: | Mermut, E., Santaclara, C., and Smith, P. |

College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |

Journal Name: | Journal of Algebra |

ISSN: | 0021-8693 |

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