Separability in algebra and category theory

@inproceedings{Wisbauer2018SeparabilityIA,
  title={Separability in algebra and category theory},
  author={R. Wisbauer},
  year={2018}
}
Separable field extensions are essentially known since the 19th century and their formal definition was given by Ernst Steinitz in 1910. In this survey we first recall this notion and equivalent characterisations. Then we outline how these were extended to more general structures, leading to separable algebras (over rings), Frobenius algebras, (non associative) Azumaya algebras, coalgebras, Hopf algebras, and eventually to separable functors. The purpose of the talk is to demonstrate that the… Expand
A CATEGORICAL APPROACH TO ALGEBRAS AND COALGEBRAS
Algebraic and coalgebraic structures are often handled independently. In this survey we want to show that they both show up naturally when approaching them from a categorical point of view. Azumaya,Expand
Object-unital groupoid graded rings, crossed products and separability
Abstract We extend the classical construction by Noether of crossed product algebras, defined by finite Galois field extensions, to cover the case of separable (but not necessarily finite or normal)Expand

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