Separating $p$-bases and transcendental extension fields
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- by J. N. Mordeson and B. Vinograde PDF
- Proc. Amer. Math. Soc. 31 (1972), 417-422 Request permission
Abstract:
Let $L/K$ denote an extension field of characteristic $p \ne 0$. It is known that if $L/K$ has a finite separating transcendence base, then every relative $p$-base of $L/K$ is a separating transcendence base of $L/K$. In this paper we show that when every relative $p$-base of $L/K$ is a separating transcendence base of $L/K$, then the transcendence degree of $L/K$ is finite. We also illustrate the connection between the finiteness of transcendence degree of $L/K$ and the property that $L/K(X)$ is separable algebraic for every relative $p$-base $X$ of $L/K$.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 417-422
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289465-9
- MathSciNet review: 0289465