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 denotes the ring of integers and denotes the field of real numbers, then is a subring of .
If is a finite field with and denotes the ring of polynomials with coefficients in , then the number of elements in the ring (of all congruence classes of polynomials modulo the polynomial ) is given by