Assignment:
Let R be a finite ring.
a. Prove that there are positive integers m and n with m > n such that xm = xn for ever x ∈ R.
b. Give a direct proof (i.e. without appealing to part c) that if R is an integral domain, then it is a field
c. Suppose that R has identity, prove that if x E R is not a zero divisor, then it is a unit.
Provide complete and step by step solution for the question and show calculations and use formulas.