Math 421/621
Spring 2000
Homework 5
a)
Show
that K is an algebraic extension of F.
b)
Show
that D is a field.
c)
Give
an examplewhere F and K are arbitrary fields and D is an integral
domain that is not a field.
a)
Show
that [F:Q]=6
b)
Exhibit
subfields of F of degrees 1,2,3 and 6 over Q.
c)
Are
there subfields of F of degree 4 or 5 over Q?
a)
b) If gcd(m,n)=1 then