## 2008.83: Pure-injective modules

2008.83:
Mike Prest
(2008)
*Pure-injective modules.*

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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 2000 > 03 Mathematical logic and foundations MSC 2000 > 16 Associative rings and algebras |

MIMS number: | 2008.83 |

Deposited By: | Professor Mike Prest |

Deposited On: | 27 September 2008 |

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