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Cotorsion-free algebras as endomorphism algebras in L - the discrete and topological cases

Rüdiger E. Göbel, Brendan Goldsmith (1993)

Commentationes Mathematicae Universitatis Carolinae

The discrete algebras A over a commutative ring R which can be realized as the full endomorphism algebra of a torsion-free R -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, V = L . Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological...

Derived equivalences between generalized matrix algebras

QingHua Chen, HongJin Liu (2020)

Czechoslovak Mathematical Journal

We construct derived equivalences between generalized matrix algebras. We record several corollaries. In particular, we show that the n -replicated algebras of two derived equivalent, finite-dimensional algebras are also derived equivalent.

Endomorphism algebras over large domains

Rüdiger Göbel, Simone Pabst (1998)

Fundamenta Mathematicae

The paper deals with realizations of R-algebras A as endomorphism algebras End G ≅ A of suitable R-modules G over a commutative ring R. We are mainly interested in the case of R having "many prime ideals", such as R = ℝ[x], the ring of real polynomials, or R a non-discrete valuation domain

Endomorphism rings of maximal rigid objects in cluster tubes

Dagfinn F. Vatne (2011)

Colloquium Mathematicae

We describe the endomorphism rings of maximal rigid objects in the cluster categories of tubes. Moreover, we show that they are gentle and have Gorenstein dimension 1. We analyse their representation theory and prove that they are of finite type. Finally, we study the relationship between the module category and the cluster tube via the Hom-functor.

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