Smith, P. F. and Vedadi, M. R.
(2008)
Submodules of Direct Sums of Compressible Modules.
*Communications in Algebra*, 36(8),
pp. 3042-3049.
(doi: 10.1080/00927870802110854)

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Publisher's URL: http://dx.doi.org/10.1080/00927870802110854

## Abstract

Let R be a ring. A right R-module M is called essentially compressible if it embeds in each of its essential submodules. Also a module X-R is called completely essentially compressible if every submodule of X-R is an essentially compressible R-module. In this aricle, it is shown that a right R-module M embeds in a direct sum of compressible right R-modules if and only if M-R is essentially compressible and every nonzero essentially compressible submodule of M-R contains a compressible submodule. Every essentially compressible R-module is shown to be retractable. Moreover, if either R-R has Krull dimension, or R is Morita equivalent to a right duo ring, then a right R-module embeds in a direct sum of compressible right R-modules if and only if it is completely essentially compressible.

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

Status: | Published |

Refereed: | Yes |

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

Authors: | Smith, P. F., and Vedadi, M. R. |

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

Journal Name: | Communications in Algebra |

ISSN: | 0092-7872 |

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