Hilbert's Theorem 90

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 then there exists in L such that The theorem takes its name from the fact that it is the 90th theorem in David Hilbert's famous Zahlbericht (Hilbert , ), although it is originally due to Kummer

Hilbert's Theorem 90

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 then there exists in L such that The theorem takes its name from the fact that it is the 90th theorem in David Hilbert's famous Zahlbericht (Hilbert , ), although it is originally due to Kummer