Large superdecomposable E(R)-algebras

Abstract

For many domains R (including all Dedekind domains of characteristic 0 that are not elds or complete discrete valuation domains) we construct arbitrarily large superdecomposableR-algebrasA that are at the same timeE(R)-algebras. Here \superde- composable means thatA admits no (directly) indecomposable R-algebra summands6 0 and \E(R)-algebra refers to the property that everyR-endomorphism of theR-module A is multiplication by an element of A.