Ring Theory: Lemma 1.6 on Uniqueness of Zero, Negative, and Identity Elements
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Questions and Answers

According to Lemma 1.6, which of the following statements about the zero element is true?

  • The zero element can have multiple values.
  • The zero element is not unique.
  • The zero element is unique. (correct)
  • The zero element is always positive.

    • Based on Lemma 1.6, what can be said about the negative of an element?

  • The negative of an element is always positive.
  • The negative of any element is unique.
  • Each element can have multiple negatives.
  • The negative of an element is not unique. (correct)

    • From Lemma 1.6, what conclusion can be drawn about the identity element in a ring?

  • The identity element is always negative.
  • The identity element is not unique.
  • The identity element is unique. (correct)
  • There can be multiple identity elements.

    • According to Lemma 1.6, what happens if a ring has two different zero elements?

    <p>The two zero elements must be the same.</p> Signup and view all the answers

    In the context of Lemma 1.6, what does having two different negatives for an element imply?

    <p>Having two negatives for an element violates ring properties.</p> Signup and view all the answers

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