MATH 462, Homework 1, problems announced in class.

1. Prove that the set {0,1} with the operations of addition and multiplication modulo 2 is a field. [Correction: the correct notation for this field is GF(2), not GL(2) as announced in class; the latter notation is used for something else. See here for more information.]
2. Give an example of a field with 3 elements.
3. Let F be a field and let S be a set. Show that the set of all functions f:S→F is a vector space over F.
4. Prove that the intersection of any two subspaces of V is a subspace.