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 |
|---|---|
| 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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