The Semigroup of Chebychev Polynomials mod 2^n

Include here an analysis of into a group of units and an ideal of nilpotent elements

Also, include here a discussion of the mod 2^n homomorphism of Cheb and Cheb[n+1] onto Cheb[n], U[n+1] onto U[n] and Nil[n+1] onto Nil[n].