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 ≠ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-1-5,
author = {Laszlo Fuchs and R\"udiger G\"obel},
title = {Large superdecomposable E(R)-algebras},
journal = {Fundamenta Mathematicae},
volume = {185},
year = {2005},
pages = {71-82},
zbl = {1096.13012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-1-5}
}
Laszlo Fuchs; Rüdiger Göbel. Large superdecomposable E(R)-algebras. Fundamenta Mathematicae, Tome 185 (2005) pp. 71-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-1-5/