Talk:Separable algebra

Wrong Theorem Name?

In the last paragraph it says There is the celebrated Jans theorem that a finite group algebra A over a field of characteristic p is of finite representation type if and only if its Sylow p-subgroup is cyclic. But I found this exact theorem in different Books under the name D.G. Higman. eg.

• Curtis, Charles W. (1962). Representation theory of finite groups and associative algebras. Pure and applied mathematics ; 11. New York [u.a.]: Interscience Publ. Page 231, Theorem 11.4.3
• Webb, Peter. (2016). A course in finite group representation theory. Cambridge studies in advanced mathematics ; 161. Cambridge: Cambridge University Press. Page 431, Theorem 64.1

The original paper most likely is Higman, D. G. (1954). Indecomposable representations at characteristic $p$. Duke Mathematical Journal, 1954, 21, 377.

Hvtka (talk) 14:03, 3 February 2019 (UTC)

Totally agree. Never heard of Jan. 2A01:599:643:804:82FA:5BFF:FE15:2B0 (talk) 06:51, 14 April 2024 (UTC)

Finiteness condition added

The article said a field extension L/K is a separable field extension iff L is a separable algebra over K. I'm pretty darn sure this is true only for extensions of finite degree (i.e. when L has finite dimension over K), since a separable algebra is a Frobenius algebra hence finite-dimensional. There are infinite-degree separable extensions of fields - often the separable closure is such - so I think we need to insert the extra finiteness condition. I did that. John Baez (talk) 19:03, 18 May 2023 (UTC)