Ring Properties of R Defined by Multiples of 4

[dash]

1. Consider the set Z of integers, and let R denote the subset all multiples of 4. Define addition as ordinary addition in Z, and define multiplication * in R by a*b = ab/4

a. Show that (R, +, *) is a ring with unity (what is the unity of R?)

b. Show that the mapping Ø: R → Z defined by Ø(x) = x/4 is an isomorphism

 

[Dick]

That looks straightforward enough. Why don't you just prove those things? What's stopping you?