Facebook Instagram Twitter RSS Feed PodBean Back to top on side

Higher degree Hilbert-symbol equivalence of number fields

In: Tatra Mountains Mathematical Publications, vol. 11, no. 2
Alfred Czogała - Andrzej Sałdek
Detaily:
Rok, strany: 1997, 77 - 88
O článku:
Harrison equivalence of degree $n$ between two fields containing a primitive $n$th root of unity is an isomorphism between the groups of $n$th power classes of these fields which preserves the norm subgroups of cyclic extension of degree $n$. Hilbert-symbol equivalence of degree $n$ between two number fields containing a primitive $n$th root of unity is an isomorphism between the groups of $n$th power classes of these fields preserving Hilbert-symbols of degree $n$. Both notions have been invented and used so far in the case $n=2$ within the theory of quadratic forms. We prove that for any prime number $n$ two global fields are Harrison equivalent if and only if they are Hilbert-symbol equivalent. This generalizes the known result for $n=2$.
Ako citovať:
ISO 690:
Czogała, A., Sałdek, A. 1997. Higher degree Hilbert-symbol equivalence of number fields. In Tatra Mountains Mathematical Publications, vol. 11, no.2, pp. 77-88. 1210-3195.

APA:
Czogała, A., Sałdek, A. (1997). Higher degree Hilbert-symbol equivalence of number fields. Tatra Mountains Mathematical Publications, 11(2), 77-88. 1210-3195.