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|
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
|Deposited By:||Professor Mike Prest|
|Deposited On:||27 September 2008|