Abstract Algebra Answers

Show that the only ideals of a field F are the trival ideal {0} and F itself

Show that the only ideal of a field F are the trival ideal {0} and F itself.

Show directly that 7Z is a maximal ideal of (Z,+,•)

Prove that the mapping : F[x] →F(a)defined by h(x)=h(a) is a homomorphism.

prove that the mapping ρ f x →f(a)defined by h(x)ρ= h(a) is a homomorphism

Define right coset of a group. Prove that there is a one-to-one correspondence

between any two right cosets of a subgroups H in a group G

Prove that the mapping p : f(x)->F(a) defined by h(x)p = h(a) is homomorphism

• prove that the mapping p:F(a)defined by h(x)p=h(a) is a homomorphism