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Cotorsion-free algebras as endomorphism algebras in \(L\) – the discrete and topological cases. (English) Zbl 0804.16031
M. Dugas and R. Göbel in 1982 investigated discrete algebras over a commutative ring \(R\) which can be realized as endomorphism algebras of torsion-free \(R\)-modules under the additional Gödel axiom of constructibility. Then they obtained many results for cotorsionfree algebras, but their proofs included rather complicated calculations in linear algebra. In this paper these results are obtained in a more simple and brief form for topological algebras. Complicated calculations in linear algebra are rejected and the results are obtained by a method which shows their natural connection with similar papers about \(p\)- groups, mixed groups, and torsion free modules over a complete discrete valuation ring.

MSC:
16S50 Endomorphism rings; matrix rings
03C60 Model-theoretic algebra
03E45 Inner models, including constructibility, ordinal definability, and core models
20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
20K20 Torsion-free groups, infinite rank
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