Local orders whose lattices are direct sums of ideals

Haefner, Jeremy

doi:10.1090/S0002-9947-1990-0978384-3

Local orders whose lattices are direct sums of ideals
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Trans. Amer. Math. Soc. 321 (1990), 717-740 Request permission

Abstract:

Let $R$ be a complete local Dedekind domain with quotient field $K$ and let $\Lambda$ be a local $R$-order in a separable $K$-algebra. This paper classifies those orders $\Lambda$ such that every indecomposable $R$-torsionfree $\Lambda$-module is isomorphic to an ideal of $\Lambda$. These results extend to the noncommutative case some results for commutative rings found jointly by this author and L. Levy.

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Unbounded dimensionality of indecomposable representations of an algebra with an infinite number of indecomposable representations

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