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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> | 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|Solution by Avi Steiner]] |
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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 $
