We prove that ℝ2 is module over Gaussian Intergers and the set of all coset of submodule in module ℝ2 over Gaussian Integers is a quotient module. We find the proof by showing that ℝ2 is both a right module and a left module over Gaussian Integers and showing that the set of all coset of submodule in module ℝ2 is both a right module and a left module over Gaussian Integers.
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