I need to show that the prime field and the prime field are in
could i get help showing one of these (the harder one) then ill try doing the other one... ??
I assume you mean the prime subfield of , notice that by definition this is the intersection of all subfields of ie. . Since and it is a field, it contains a copy of . Now is the field of fractions of so is the smallest field containing , so and since ...
wow i was completely off on the question.. sorry.
i) Show that every subfield of contains
I thought was a subfield of but there is no subfield of ... but wouldn't that disprove this statement... units are 1,-1,i,-i )
ii) Show that the prime field of is
iii) Show that the prime field of is