Student solutions for Assignment #3

Solution Sample

Problem 50

Problem 50 - Tan Dang

Problem 94

Show $f (x) = x 4 + 5 x 2 + 3 x + 2$ is irreducible over the field of rational numbers.

Solution by Nicole_Rutt

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 $\mathbb{Z}_3[x]$

Solution

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 $R$

Solution by Avi Steiner

Problem 114

A local ring is a commutative ring with 1 that has a unique maximal ideal. Show that a ring R is local if and only if the set of non-units in R is an ideal.

kiwi.ecn.purdue.edu/rhea/images/c/ca/Problem_114_Kent_State_Algebra_Qual_Ring.pdf

Back to 2013 Summer MA 598A Weigel

Assignment - Rhea

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