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Answer to Question #16816 in Algebra for sanches

Question #16816
If m and m' are maximal right ideals in a ring R, show that the (simple) right R-modules R/m and R/m' are isomorphic iff there exists an element r ∈ R\m such that rm' ⊆ m. In this case, show that m and m' contain exactly the same ideals of R.
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