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Construction of Auslander-Gorenstein local rings as Frobenius extensions

Mitsuo Hoshino, Noritsugu Kameyama, Hirotaka Koga (2015)

Colloquium Mathematicae

Starting from an arbitrary ring R we provide a systematic construction of ℤ/nℤ-graded rings A which are Frobenius extensions of R, and show that under mild assumptions, A is an Auslander-Gorenstein local ring if and only if so is R.

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...

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