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#hilbert's_theorem_90

Hilbert's Theorem 90

Result due to Kummer on cyclic extensions of fields that leads to Kummer theory

In abstract algebra, Hilbert's Theorem 90 (or Satz 90) is an important result on cyclic extensions of fields (or to one of its generalizations) that leads to Kummer theory. In its most basic form, it states that if L/K is an extension of fields with cyclic Galois group G = Gal(L/K) generated by an element and if is an element of L of relative norm 1, that is

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Hilbert's Theorem 90 Hilbert's theorem David Hilbert Hilbert space List of theorems Galois cohomology Artin–Schreier theory List of things named after David Hilbert Zahlbericht Class formation
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