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Let A$A$ be a finite dimensional k$k$-algebra and let I$I$ be an injective module。My question is whether I$I$ is a direct sum of finite dimensional-dimensional injective modules。

Let A be a finite dimensional k-algebra and let I be an injective module。My question is whether I is a direct sum of finite dimensional injective modules。

Let $A$ be a finite dimensional $k$-algebra and let $I$ be an injective module。My question is whether $I$ is a direct sum of finite-dimensional injective modules。

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Injective modules

Let A be a finite dimensional k-algebra and let I be an injective module。My question is whether I is a direct sum of finite dimensional injective modules。