General Directions: Written assignments should be submitted typeset. What you submit must represent your own work.
Read these directions carefully: For each of the following statements either provide a proof that the statement is true or label the statement as false and provide justification.
If Z denotes the ring of integers and R denotes the field of real numbers, then
{a + b SQRT[3]{2} \in R | a, b \in Q} |
is a subring of R.
If F is a finite field with |F| = q and F [t] denotes the ring of polynomials with coefficients in F, then the number of elements in the ring
A = F [t] / (t^{q} - t) F [t] |
(of all congruence classes of polynomials modulo the polynomial t^{q} - t) is given by
|A| = q^{q} . |