This group gathers theorems about fields and their extensions, the algebraic setting in which one adds, subtracts, multiplies and divides, and about Galois theory, which links field extensions to groups of symmetries. It covers questions such as when a single element generates a whole extension, when an equation can be solved by radicals, and how the lattice of intermediate fields matches the lattice of subgroups. A theorem belongs here when its cited article places it in field theory, field extensions or Galois theory.
All Field Theory and Galois Theory
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Fundamental Theorem of Galois Theory (Wikipedia)
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In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain
Abel-Ruffini Theorem (Wikipedia)
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polynomial. This improved statement follows directly from Galois theory § A non-solvable quintic example. Galois theory
Primitive element theorem (Wikipedia)
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In field theory, the primitive element theorem states that every
Hilbert's Theorem 90 (Wikipedia)
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Theorem 90 (or Satz 90) is an important result on cyclic extensions of fields (or to one of its generalizations) that leads
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