There is a sort of arithmetic of ideals in a ring. The exercises define sum, product, and
Question:
There is a sort of arithmetic of ideals in a ring. The exercises define sum, product, and quotient of ideals.
Let A and B be ideals of a ring R. The product AB of A and B is defined by
a. Show that AB is an ideal in R.
b. Show that AB ⊆ (A ∩ B).
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a It is clear that AB is closed under addition a sum of m products of the form a i b i a sum of n ...View the full answer
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