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Finitely-generated algebra
If E/F is a finite field extension then it follows from the definitions that E is a finitely generated algebra over F. Conversely, if E /F is a field extension and E is a ...
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1. Classification of finitely generated field extensions. The following problem will be the main focus of these lectures: Problem 1.1. Fix a field K. Classify all finitely ...
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Apr 22, 2011 ... If $F=K(u_1,\ldots,u_n)$ is a finitely generated extension of $K$ and $M$ is an intermediate field, then $M$ is a finitely generated extension of ...
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of real numbers, but is obviously an infinite set), and it is not even equivalent to " finitely generated" (a transcendental extension is never a finite extension, but it ...
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May 30, 2011 ... Finitely Generated Algebraic Extension is Finite ... Let $L/K$ be a field extension and $\alpha_1,\ldots,\alpha_n \in L$ algebraic over $K$.
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generated difference field extensions are finitely generated (Theorem 1). ... closure of a finitely generated extension of X, then Theorem 1 implies the following ...
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complex coefficients has no finitely generated pathological extensions. In §3 we ... we assume that every extension is finitely generated and of order zero. As ...
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Apr 12, 2010 ... As Brian Conrad remarked above, subextensions of finitely generated extensions are also finitely generated. Here is a prove. I wish there ...
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Computational Ideal Theory in Finitely. Generated Extension Rings. Joachim Apel. Fakult at f ur Mathematik und Informatik, Universit at Leipzig. Augustusplatz ...
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May 29, 2011 ... A fact about finitely generated field extensions. Let F be a field and let E be an extension of F . Suppose E is finitely generated as an F -vector ...
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