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SOLVED: For each natural number, let R be a ring. Define the infinite direct sum R = R1 ⊕ R2 ⊕ R3 ⊕ ... to be the set of all sequences of
SOLVED: EXERCISES (0) Let G be an (additive) abelian group. Define an operation of multiplication, denoted by *, on G. Then G is a ring. (6) Let be the set of all
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Short Essay: Ideals of Direct Products Let R × S be a direct product of rings. Then any ideal of R × S is I × J, for some ide
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SOLVED: Answer the following with true (T) or false (F): The direct product of two rings with the same characteristic is a ring with no characteristic. A ring R with a =
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