SS, +, >, and a field F := F, +, . >. (a) Prove that the integral domain D is a field if and only if each equation ax = b for a, b € D and a 0 has a unique solution in D. (b) Given a ring S. For each s € S define a mapping og : SS by o(a) = s. a for each a € S. If S is a commutative ring, explain why Ker o, ‡ {0} if and only if s = 0 or s is a zero divisor in S. (c) For S a field and s‡0, explain why σ, defined in (b) is an isomorphism of the additive group of S onto itself.

sorry I should of been clear, I need letter B to be worked out.

This is part two of a question already asked. I have provided the answer sent, now there is a part 2 to the problem...its shown in picture 2.Part 2 is needed.

Can i share my screen and show you a homework problem that I thought I did right but is wrong and I don't know what I've done wrong?

Please help me answer the following questions. Thank you

Question is attached