There is a sort of arithmetic of ideals in a ring. The exercises define sum, product, and

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There is a sort of arithmetic of ideals in a ring. The exercises define sum, product, and quotient of ideals.

If A and B are ideals of a ring R, the sum A + B of A and B is defined by A+ B = {a+ b | a ∈ A, b ∈ B}.

a. Show that A + B is an ideal.

b. Show that A ⊆ A + B and B ⊆ A + B.

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A First Course In Abstract Algebra

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There is a sort of arithmetic of ideals in a ring. The exercises define sum, product, and

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A First Course In Abstract Algebra

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