Is the set {a + bw/ga, b ∈ Z} a ring? Justify your answer.
Added by Deborah S.
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Addition: Let x = a + bw/ga and y = c + dw/gc be two elements in the set. Then, x + y = (a + c) + (bw/ga + dw/gc) = (a + c) + bwd/gagc. Since b and g are integers, bwd is also an integer. Therefore, x + y is in the set. Multiplication: Let x = a + bw/ga and y Show more…
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