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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Separating $ p$-bases and transcendental extension fields


Authors: J. N. Mordeson and B. Vinograde
Journal: Proc. Amer. Math. Soc. 31 (1972), 417-422
MathSciNet review: 0289465
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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$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0289465-9
Keywords: Extension fields, separating transcendence bases, relative $ p$-bases
Article copyright: © Copyright 1972 American Mathematical Society