Pure-injective modules

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

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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
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: https://eprints.maths.manchester.ac.uk/id/eprint/1148

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