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- W2949638560 abstract "Let $R$ be a commutative ring with identity and $D$ an $R$-module. It is shown that if $D$ is pure injective, then $D$ is isomorphic to a direct summand of the direct product of a family of finitely embedded modules. As a result, it follows that if $R$ is Noetherian, then $D$ is pure injective if and only if $D$ is isomorphic to a direct summand of the direct product of a family of Artinian modules. Moreover, it is proved that $D$ is pure injective if and only if there is a family ${T_lambda}_{lambdain Lambda}$ of $R$-algebras which are finitely presented as $R$-modules, such that $D$ is isomorphic to a direct summand of a module of the form $Pi_{lambdain Lambda}E_lambda$ where for each $lambdain Lambda$, $E_lambda$ is an injective $T_lambda$-module." @default.
- W2949638560 created "2019-06-27" @default.
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- W2949638560 date "2005-09-22" @default.
- W2949638560 modified "2023-09-27" @default.
- W2949638560 title "Two characterizations of pure injective modules" @default.
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