Titlebook: Lectures in Abstract Algebra; III. Theory of Field Nathan Jacobson Textbook 1964 Springer Science+Business Media, LLC 1964 Abstract algebra

BACLE

Galois Theory of Equations, fields is interesting also beyond the theory of equations and we shall undertake a detailed study of such fields in the next chapter. In the present one we confine ourselves to the minimum which is needed for the theory of equations.

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Structure Theory of Fields,xistence of a transcendency basis such that the extension is separable algebraic over the purely transcendental extension determined by the basis. We shall also give a definition of separability of an extension field that generalizes the notion of algebraic separability. The notion of a derivation p

火海

Valuation Theory,ions. Valuation theory forms a solid link between algebra and analysis. On the one hand, it permits a precise study of algebraic functions and, on the other hand, it leads to the introduction of analytic notions (convergence, integration) in the study of arithmetic questions.

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Lectures in Abstract Algebra978-1-4612-9872-4Series ISSN 0072-5285 Series E-ISSN 2197-5612