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== Problem 94 == | == Problem 94 == | ||
| − | Show f(x) = | + | Show <math>f(x) = x^4 + 5x^2 + 3x + 2</math> is irreducible over the field of rational numbers. |
| − | *[[Media:Problem_94_-_Nicole_Rutt.pdf| Solution by Nicole_Rutt]] | + | *[[Media:Problem_94_-_Nicole_Rutt.pdf| Solution by Nicole_Rutt]] |
== Problem 101 == | == Problem 101 == | ||
Revision as of 06:13, 25 June 2013
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 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 $
