Two examples of local Artinian rings

Xue, Wei Min

doi:10.1090/S0002-9939-1989-0979222-2

Two examples of local Artinian rings
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Proc. Amer. Math. Soc. 107 (1989), 63-65 Request permission

Abstract:

We answer a question of D. A. Hill in the negative by providing two local artinian rings $R$ and $S$ such that $R$ is right serial but the left indecomposable injective $R$-module is not uniserial, and that $S$ is not right serial but the left indecomposable injective $S$-module is uniserial. Moreover $R$ possesses a Morita duality but fails to have self-duality.

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