Hi again :

I have an exercise a little complicated and extensive,

Let be the direct product of copies of indexed with the positive integers (so A is a ring under componentwise addition and multiplication) and let R be the ring of all group homomorphism from A to itself with addition defined as pointwise addition of functions . If be the element of R defined by . Now , if be the element of R defined by . Prove that :

a) (composition functions) is the identity of R ,but is not the identity of R (i.e is a right inverse for , but not a left inverse.

b)Exhibit infinitely many right inverses for

c)Find a nonzero element R such that , but

d)Prove that is no nonzero element p R such that (i,e

is a left zero divisor but not a right zero divisor)

Any help will be well welcome

Thanks