Are biseparable extensions Frobenius?

DOI10.1023/A:1014039026760zbMath1007.16011arXivmath/0104019OpenAlexW1978617540MaRDI QIDQ1611336

Lars Kadison, Stefaan Caenepeel

Publication date: 21 August 2002

Published in: \(K\)-Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0104019

zbMATH Keywords

projective modulesFrobenius algebrasFrobenius functorsseparable functorsseparable algebrasseparable bimodulesFrobenius bimodulesbiseparable extensionsFrobenius ring extensionsseparable ring extensionssplit ring extensions

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Free, projective, and flat modules and ideals in associative algebras (16D40) Quasi-Frobenius rings (16L60) Bimodules in associative algebras (16D20) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

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Frobenius bimodules between noncommutative spaces. ⋮ FROBENIUS FUNCTORS OF THE SECOND KIND ⋮ Representable Functors for Corings ⋮ Uniquely separable extensions ⋮ Naturally full functors in nature. ⋮ Bialgebroid actions on depth two extensions and duality. ⋮ Biseparable extensions are not necessarily Frobenius ⋮ Formally smooth bimodules. ⋮ Comodules and Corings ⋮ Quasi-Frobenius Corings and Quasi-Frobenius Extensions ⋮ Separable equivalence of rings and symmetric algebras ⋮ Depth Two, Normality, and a Trace Ideal Condition for Frobenius Extensions ⋮ When ∏ is Isomorphic to ⊕ ⋮ An approach to Hopf algebras via Frobenius coordinates. II ⋮ Maschke functors, semisimple functors and separable functors of the second kind: applications ⋮ Separable bimodules and approximation.

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