Let F be a field of characteristic O and R = F[x,y] the additive group of polynomials in two indeterminates. Define multiplication in R by requiring that multiplication be distributive, that ax = xa, ay = ya for all a ϵ F, that the product of x and y (in that order) be the polynomial xy as usual, but that the product of y and x be the polynomial xy + I. 

(a) R is a ring.

(b) yx^k = x^ky + kx^k-1 and y^kx = xy^k + ky^k-1

(c) R is simple.

(d) R has no zero divisors.

(e) R is not a division ring.