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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. | 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. | ||
| − | [https://kiwi.ecn.purdue.edu/rhea/images/c/ca/Problem_114_Kent_State_Algebra_Qual_Ring.pdf | + | [https://kiwi.ecn.purdue.edu/rhea/images/c/ca/Problem_114_Kent_State_Algebra_Qual_Ring.pdf Solution by Nathan Moses]<br> |
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Revision as of 14:19, 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 $ \mathbb{Z}_3[x] $.
(b) Show that x4 + 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
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.
