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Abstract Algebra Tasks

Task:
A. Use the definition for a ring to prove that Z7 is a ring under the operations + and × defined as follows:
[a]7 + [b]7 = [a + b]7 and [a]7 × [b]7 = [a × b]7
Note: On the right-hand-side of these equations, + and × are the usual operations on the integers, so the modular versions of addition and multiplication inherit many properties from integer addition and multiplication...

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