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2008.83: Pure-injective modules

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

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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 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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