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Multiple Choice

Let $R$ be a ring and $M$ be a left $R$-module. Which of the following statements is true?

  1. The set of all submodules of $M$ forms a group under the operation of addition.
  2. The set of all submodules of $M$ forms a ring under the operation of addition and multiplication.
  3. The set of all submodules of $M$ forms a field under the operation of addition and multiplication.
  4. The set of all submodules of $M$ forms a vector space over the field of real numbers.
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