I've got to show the binary structure <nZ,+> is an abelian group where n is an integer?

Question

I know i have to show it is commutative....any suggestions

Answer 1

Take 2 arbritrary elements, nx and ny. Add them together: nx+ny=n(x+y), x and y are in Z, and Z is communtative, so we have =n(y+x)=ny+nx, hence abelian. To show that it is a group, you need to use the definition and use the arbritray elements. This is for the group. I noticed that you used the words abelian and commutative, are you looking at showing the ring is commutative? If so, is the multiplication the usual multiplication? The proof to show that the multiplication is commutative is the same, except that you have multiplication verses addition. Hope this helps.