Timeline for Symmetrizing with respect to Galois Group: Trace and Norm

6 events

when toggle format	what		by	license	comment
May 17, 2017 at 9:54	answer	added	Doris		timeline score: 1
Apr 25, 2017 at 3:20	history	edited	Myshkin	CC BY-SA 3.0	+ top level tag (nt.)
Apr 25, 2017 at 2:50	comment	added	Tom Goodwillie		But you can think of another generator of the cyclotomic field such that its trace is rational. For example, in the $8$th cyclotomic field $\zeta+\zeta^2+\zeta^3$.
Apr 25, 2017 at 2:37	comment	added	P Vanchinathan		Thats my point: Using N, Tr, for relative norm and trace: $N(\zeta)$ and $N(1+\zeta)$ have different degrees as algebraic numbers. But Tr($\zeta$) and Tr($1+\zeta$) have same degrees.
Apr 25, 2017 at 0:51	comment	added	Tom Goodwillie		There is no real asymmetry. It just happens that $\zeta\bar\zeta$ is rational. But use $\alpha=1+\zeta$ instead and you get $\alpha\bar\alpha=2+\zeta+\bar\zeta$.
Apr 25, 2017 at 0:35	history	asked	P Vanchinathan	CC BY-SA 3.0