Contents
Student solutions for Assignment #3
Problem 50
Problem 94
Show $ f(x) = x^4 + 5x^2 + 3x + 2 $ is irreducible over the field of rational numbers.
Problem 101
(a) Show that $ x^4 +x^3 +x^2 +x+1 $ is irreducible in $ \mathbb{Z}_3[x] $.
(b) Show that $ x^4 + 1 $ is not irreducible in $ \mathbb{Z}_3[x] $
Problem 107
Let $ R $ be a commutative ring with identity such that the identity map is the only ring automorphism of $ R $. Prove that the set $ N $ of all nilpotent elements of $ R $ is an ideal of $ R $
