Kaplansky's radical and Hilbert Theorem 90. III
Tatsuo Iwakami, Daiji Kijima, Mieo Nishi · Hiroshima Mathematical Journal · 1985
Let F be a field, R(F) be Kaplansky's radical of F and K = F(ja) be a quadratic extension of F. We showed in [4], that if F is a quasi-pythagorean field and K is a radical extension (i.e. a eK(F)-F 2 ), then K is also quasi-pythagorean and the 'H-conjecture' N-1 (R(F)) = F-R(K) is valid, where N: K-+F is the norm map.In this paper we generalize the above results and show that the //-conjecture is valid whenever K is a quasi-pythagorean field.