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... ??

Printable View

- November 23rd 2009, 10:42 AMux0prime field
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... ?? - November 23rd 2009, 11:24 AMJose27
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 ...

- November 23rd 2009, 07:24 PMux0
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 - November 23rd 2009, 10:23 PMJose27
Read carefully my first post and you'll notice that it answers all three questions.

As for this is, by definition, the smallest ring that contains both and , and is the aboves fraction field, and since it contains it must contain - November 24th 2009, 01:18 AMShanks
Yeah, Jose27 is quite right.

- November 24th 2009, 08:08 AMux0