this exercise shows that every ring R can be enlarged to a ring S with unity, having the same characteristics as R. Let

[answerhappygod]

this exercise shows that every ring R can be enlarged to a ring
S with unity, having the same characteristics as R. Let S=RxZ if R
has characteristic 0 and RxZn if R has characteristic n. Let
addition in S be the usual addition by components and let
multiplications be defined by where nxr has the meaning explained
in section 22
show that S is a ring
show that S has unity
Show that S and R have the same characteristic