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== Problem 94 == | == Problem 94 == | ||
| − | *[[Media:Problem_94_-_Nicole_Rutt.pdf| | + | Show f(x) = x4 + 5x2 + 3x + 2 is irreducible over the field of rational numbers. |
| + | *[[Media:Problem_94_-_Nicole_Rutt.pdf| Solution by Nicole_Rutt]] | ||
== Problem 101 == | == Problem 101 == | ||
| − | *[[Media:Week_3_Problem_101.pdf| | + | (a) Show that x4 +x3 +x2 +x+1 is irreducible in Z3[x]. |
| + | |||
| + | (b) Show that x4 + 1 is not irreducible in Z3[x]. | ||
| + | |||
| + | *[[Media:Week_3_Problem_101.pdf| Solution]] | ||
== Problem 107 == | == Problem 107 == | ||
| + | Let <math>R</math> be a commutative ring with identity such that the identity map is the only ring automorphism of <math>R</math>. Prove that the set <math>N</math> of all nilpotent elements of <math>R</math> is an ideal of <math>R</math> | ||
| + | |||
*[[Assn3Prob107]] | *[[Assn3Prob107]] | ||
Revision as of 05:33, 25 June 2013
Contents
Student solutions for Assignment #3
Problem 50
Problem 94
Show f(x) = x4 + 5x2 + 3x + 2 is irreducible over the field of rational numbers.
Problem 101
(a) Show that x4 +x3 +x2 +x+1 is irreducible in Z3[x].
(b) Show that x4 + 1 is not irreducible in Z3[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 $
