Question: Let (R, +, ) be a ring with unity u, and |R| = 8. On R4 = R R R R, define

Let (R, +, •) be a ring with unity u, and |R| = 8. On R4 = R × R × R × R, define + and • as suggested by Exercise 18. In the ring R4,
(a) How many elements have exactly two nonzero components?
(b) How many elements have all nonzero components?
(c) Is there a unity?
(d) How many units are there if R has four units?

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