LetRbe a ring with unity 1 andnan integer. Define

n· 1 =

{1 + 1 + . . . + 1 tonterms ifn> 0

0 ifn= 0

−1 + (−1) + . . . + (−1) to |n| terms ifn< 0

(a) Show that ψ : Z →Rgiven by

ψ (n) =n· 1

is a ring homomorphism.

(b) Find know rings which are possible images of ψ.