Assignment:
Consider the set R={0,2,4,6,8} ⊆ Z10.
a) Construct addition and multiplication tables for R, using the operations in Z10.
b) Is R a commutative ring? Does it have unity and, if so, which element is unity?
c) Does R have zero divisors?
d) Which elements of R have multiplicative inverses?
Provide complete and step by step solution for the question and show calculations and use formulas.