A counterexample concerning inseparable field extensions
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- by James Kevin Deveney PDF
- Proc. Amer. Math. Soc. 55 (1976), 33-34 Request permission
Abstract:
Let $K \supseteq M \supseteq k$ be a chain of fields of characteristic $p \ne 0$ where $K$ is separable over $M$ and $M$ is purely inseparable over $k$. Recently it has been shown that if $K$ has a separating transcendency basis over $M$ or if $M$ is of bounded exponent over $k$, then $K = M{ \otimes _k}S$ where $S$ is separable over $k$. This note presents an example to show that, in general, no such $S$ need exist.References
- H. F. Kreimer and N. Heerema, Modularity vs. separability for field extensions, Canadian J. Math. 27 (1975), no. 5, 1176–1182. MR 392951, DOI 10.4153/CJM-1975-123-2
- Nickolas Heerema and David Tucker, Modular field extensions, Proc. Amer. Math. Soc. 53 (1975), no. 2, 301–306. MR 401724, DOI 10.1090/S0002-9939-1975-0401724-8
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 55 (1976), 33-34
- DOI: https://doi.org/10.1090/S0002-9939-1976-0396509-6
- MathSciNet review: 0396509