Infinite Field Extensions

P. M. Cohn
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P. M. Cohn: University College London, Department of Mathematics

Chapter 11 in Basic Algebra, 2003, pp 397-447 from Springer

Abstract: Abstract Chapter 7 was almost entirely devoted to field extensions of finite degree and concentrated on Galois theory . However, even an introductory account should make some mention of infinite field extensions, and we shall discuss them in the present chapter, including transcendental extensions (Section 11.3) and infinite Galois theory (Section 11.8). The notion of algebraic dependence has similarities to linear dependence, which are described in abstract form in Section 11.1 and applied in Section 11.2. In addition there are concise accounts of topics that are useful in commutative ring theory and algebraic geometry, besides being of independent interest : separability (Sections 11.4 and n .s), the interactions of two or more subfields (Sections 11.6 and 11.7), applications of Galois theory (Section 11.9) and abelian extensions of finite exponent (Section 11.10).

Keywords: Prime Ideal; Galois Group; Dependence Relation; Algebraic Closure; Minimal Polynomial (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-0-85729-428-9_11

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