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Welcome to our world of fun trivia quizzes and quiz games:
An Adventure in Abstract Algebra
"If you think a ring is something you wear on your finger, a group is you and your friends, and a field is for playing baseball - this quiz is not for you. These are eight basic facts and two calculations from abstract (modern) algebra."
15 Points Per Correct Answer - No time limit
What property is not found in every ring?
Closure under addition and multiplication
A group of this order is NOT guaranteed to be Abelian.
What group can be written as: (123), (132), (213), (231), (312), (321)?
C3 x C3
A group of order 150 cannot have a subgroup of this order.
What extension field is the algebraic closure for the reals?
The complex numbers
A commutative ring where AxB=0 implies that A=0 or B=0 is called what?
An integral domain
A unique factorization domain
A principal ideals domain
Which of these sets is an ideal in the ring of integers?
The negative numbers
The odd numbers
The even numbers
The positive numbers
What is the degree of the splitting field of the polynomial X^3 - 2 over the rationals?
What is the Galois group for the splitting field Q[sqrt(2)+sqrt(3)]?
C2 x C2
The dihedral group of a pentagon
Under Galois theory, the roots of a polynomial is solvable by radicals if and only if the polynomial's Galois group is . . .
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Compiled May 22 13