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Large superdecomposable E(R)-algebras

Laszlo FuchsRüdiger Göbel — 2005

Fundamenta Mathematicae

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.

On a class of submodules in direct products

Laszlo FuchsFrans Loonstra — 1976

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

In una somma diretta finita di moduli, i sottomoduli possono costruirsi usando certi omomorfismi e certe equazioni. Nel presente lavoro si studiano quei sottomoduli che possono ottenersi in modo simile in un prodotto infinito di moduli.

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