# I need help fixing my work for the following question : Rings

are an important algebraic structure, and modular arithmetic has that structure. Recall that for the mod m relation, the congruence class of an integer x is denoted [x]m. For example, the elements of [–5]7 are of the form –5 plus integer multiples of 7, which would equate to {. . . –19, –12, –5, 2, 9, 16, . . .} or, more formally, {y: y = -5 + 7q for some integer q}. 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 B. Use the definition for an integral domain to prove that Z7 is an integral domain. My submission and the comments from my grader are attached.

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