The identity element on the set &DoubleStruckZEE; of integers under the binary operation '' defined by a * b = a + b + 1 ∀ a, b ∈ &DoubleStruckZEE; is:

In the polynomial ring &mathbb;Q[x], if f(x) = x3 + x2 + x + 1 and g(x) = x3 - x2 + x - 1, then the ideal ⟨f(x), g(x)⟩ generated by f(x) and g(x) is equal to:

Which of the following algebraic structures forms an Abelian group under the usual operation?