Consider the ring R = {f($) E Q[a:] : f(0) E Z}. 1. Show that R is an integral domain and that RX 2 {1, 1}. 2. Show that the irreducible elements in R are a prime constant polynomials :|:p E Z, or o irreducible polynomials f (at) E QM such that f (0) = :|:1. 3. Show that 1: cannot be written as a nite product of irreducible elements of R. (In particular, show :19 is not itself irreducible.) 4. Show that a: is not prime in R. [Hint: If it helps describe R/ (51:)]