Question: For R = {s, t, x, y}, define + and , making R into a ring, by Table 14.5(a) for + and by the partial

For R = {s, t, x, y}, define + and , making R into a ring, by Table 14.5(a) for + and by the partial table for + in Table 14.5(b).

(a) Using the associative and distributive laws, determine the entries for the missing spaces in the multiplication table.
(b) Is this ring commutative?
(c) Does it have a unity? How about units?
(d) Is the ring an integral domain or a field?

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