Prest, Mike
(2008)
*Pure-injective modules.*
[MIMS Preprint]

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## Abstract

The pure-injective $R$-modules are defined easily enough: as those modules which are injective over all pure embeddings, where an embedding $ A\rightarrow B $ is said to be pure if every finite system of $ R$-linear equations with constants from $ A $ and a solution in $ B $ has a solution in $ A. $ But the definition itself gives no indication of the rich theory around purity and pure-injectivity. The purpose of this survey is to present and illustrate the definitions and a number of the results around pure-injective modules.

Item Type: | MIMS Preprint |
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Additional Information: | A short survey |

Uncontrolled Keywords: | pure-injective, algebraically compact, module |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras |

Depositing User: | Professor Mike Prest |

Date Deposited: | 27 Sep 2008 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/1148 |

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