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## 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 A short survey pure-injective, algebraically compact, module MSC 2000 > 03 Mathematical logic and foundationsMSC 2000 > 16 Associative rings and algebras 2008.83 Professor Mike Prest 27 September 2008