Large superdecomposable $E(R)$-algebras
Volume 185 / 2005
Fundamenta Mathematicae 185 (2005), 71-82
MSC: Primary 13F99, 13C13; Secondary 03E05.
DOI: 10.4064/fm185-1-5
Abstract
For many domains $R$ (including all Dedekind domains of characteristic 0 that are not fields or complete discrete valuation domains) we construct arbitrarily large superdecomposable $R$-algebras $A$ that are at the same time $E(R)$-algebras. Here “superdecomposable” means that $A$ admits no (directly) indecomposable $R$-algebra summands $ \ne 0$ and “$E(R)$-algebra” refers to the property that every $R$-endomorphism of the $R$-module ,$A$ is multiplication by an element of ,$A$.
