Basic Algebra test

Do you think you know algebra? Take this basic algebra test. I DARE YOU! Oh well, don't do it if you don't want to. Random answers are for weak people.

Algebra is not just solving simple polynomial stuff. Take this test and check how low your score is. Definitions are in wikipedia. Random answers are for weak people.

Created by: Hurr durr
  1. Every finite integral domain is a field.
  2. Which of the following is an irreducible polynomial over the integers
  3. Let f: G ---> H be a homomorphism between groups (H is an abelian group). Which of the following is not a true statement?
  4. How many integer solutions does 5x+10y+20z = 12 have?
  5. Let F be a field. Let V be a F-vectorial space of dimension 3. Let W be a F-vectorial space of dimension 4. Let X be the set of linear transformations from V to W, X is a F-vectorial space. What is the dimension of X?
  6. How many fields lies between the reals and the complex numbers?
  7. Let G be a group with 6 elements. Which of the following can't be true.
  8. Let C be the set of 2x2 matrices of the form (a -b;b a) (a,b real numbers). Which of the following is false:
  9. Let p be a prime number. Let G be a group of order p^2. Which of the following must be true.
  10. Every field has a subfield isomorphic to the rational numbers, or there exist a prime number p such that theres a subfield isomorphic to Z/pZ

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