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Part II: Solve the following problems. Justify all answers with rigorous, clear explanations. 4. Let R be a commutative ring with 1 and let

Part II: Solve the following problems. Justify all answers with rigorous, clear explanations. 4. Let R be a commutative ring with 1 and let r be an element of R. (a) Show that if r is a unit then r and r` are also units. -1 (b) Show that if r and s are units, then rs is also a unit.

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