Injective modules and semistar operations
The author classify injective modules over an integral domains by considering the class of semistar noetherian domains. The main result states that if \(*\) is a semistar operation over a domain \(R\), then every injective module \(H\) admits a direct composition \(H=A\bigoplus B\bigoplus C\) where \(A\) is the injective hull of the \(*\)-null part \(\tau_{*}H\), \(B\) is the injective hull of a maximal co-\(*\)-submodule of \(H\) and \(C\) is \(*\)-neutral. Moreover, if \(R\) is \(*\)-noetherian, the structure of \(B\) is described and a complete classification of the injective hulls of co-\(*\)-modules is obtained.
scientific article; zbMATH DE number 5999987
scientific article