Ring Definitions and Basic Properties Quiz
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Questions and Answers

Which of the following rings is a commutative ring?

  • (ℤ𝑖, +,∙) (correct)
  • (𝑀2 ℝ, +,∙)
  • (𝑀2 ℤ, +,∙)
  • (𝑀2 ℚ, +,∙)

    • Which of the following is an example of a non-commutative ring with identity?

  • (𝑀2 ℝ, +,∙)
  • (𝑀2 ℚ, +,∙)
  • (𝑀2 ℤ, +,∙) (correct)
  • (ℤ𝑖, +,∙)

    • Which product defines the remainder of the usual product of integers when divided in the cyclic group (ℤ𝑛 , +)?

  • $a + b$
  • $a \cdot b$ (correct)
  • $a - b$
  • $a^2$

    • Which of the following rings is an infinite ring?

    <p>ℤ (B)</p> Signup and view all the answers

    When is a ring called a finite ring?

    <p>When it has only a finite number of elements (D)</p> Signup and view all the answers

    What is the significance of the number 365 in the text?

    <p>It represents the number of days in a year (A)</p> Signup and view all the answers

    What does the text suggest about the star 'Alshar'?

    <p>It is visible for 365 days in a year (B)</p> Signup and view all the answers

    What is the significance of '12' in the context of 'Alshar'?

    <p>It represents the number of months in a year (D)</p> Signup and view all the answers

    What does the text imply about the importance of 'Al-Najm Al-Sha'ary Al-Yamani'?

    <p>It holds significance in Yemeni astronomy and poetry (D)</p> Signup and view all the answers

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