An Adventure in Abstract Algebra

15 Points Per Correct Answer - No time limit  

1. What property is not found in every ring? Associative addition Commutative multiplication Distributive rule Closure under addition and multiplication

2. A group of this order is NOT guaranteed to be Abelian. 9 5 169 125

3. What group can be written as: (123), (132), (213), (231), (312), (321)? A6 D6 S3 C3 x C3

4. A group of order 150 cannot have a subgroup of this order. 1 8 5 6

5. What extension field is the algebraic closure for the reals? The reals The quaternions The rationals The complex numbers

6. A commutative ring where AxB=0 implies that A=0 or B=0 is called what? Euclidian An integral domain A unique factorization domain A principal ideals domain

7. Which of these sets is an ideal in the ring of integers? The negative numbers The odd numbers The even numbers The positive numbers

8. What is the degree of the splitting field of the polynomial X^3 - 2 over the rationals? 2 6 3 1

9. What is the Galois group for the splitting field Q[sqrt(2)+sqrt(3)]? C2 x C2 S5 The quarternions The dihedral group of a pentagon

10. Under Galois theory, the roots of a polynomial is solvable by radicals if and only if the polynomial's Galois group is . . . solvable. cyclic. Abelian. prime.