What Do You Know About Shapiro's Lemma?

10 Questions | Total Attempts: 108

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What Do You Know About Shapiro

Also known as the Eckmann–Shapiro Lemma, Shapiro's lemma is useful in numerous areas of the abstract algebra field in mathematics. In the 21st century, Beno Eckmann and Arnold Shapiro individually contributed to the realization of this concept, which relates extensions of modules over one ring to extensions over another. This especially works best in the group ring of a group and of a subgroup.


Questions and Answers
  • 1. 
    Shapiro's lemma is also known as which of these?
    • A. 

      Eckmann Lemma

    • B. 

      Eckmann—Shapiro Lemma

    • C. 

      Erick—Shapiro Lemma

    • D. 

      Erick Lemma

  • 2. 
    Who proved the theorem? 
    • A. 

      Arnold Shapiro

    • B. 

      Alfred Shapiro

    • C. 

      Josh Shapiro

    • D. 

      Matt Shapiro

  • 3. 
    When was the theorem proven?
    • A. 

      1961

    • B. 

      1962

    • C. 

      1963

    • D. 

      1964

  • 4. 
     Who first discovered the theorem? 
    • A. 

      Beno Erick

    • B. 

      Alfred Eckmann

    • C. 

      Beno Eckmann

    • D. 

      Alfred Erick

  • 5. 
    When was the theorem discovered? 
    • A. 

      1951

    • B. 

      1952

    • C. 

      1953

    • D. 

      1954

  • 6. 
    What does R → S  denote?
    • A. 

      Ring homomorphism

    • B. 

      Ring endomorphism

    • C. 

      Ring

    • D. 

      Ring and Satellite

  • 7. 
    What does M denote?
    • A. 

      Right S-module

    • B. 

      Left S-module

    • C. 

      Left M-module

    • D. 

      Right M-module

  • 8. 
    What does N denote?
    • A. 

      Left R-module

    • B. 

      Right R-module

    • C. 

      Left N-module

    • D. 

      Right N-module

  • 9. 
    What does S denote?
    • A. 

      Left and right S-module

    • B. 

      Left and right R-module

    • C. 

      Left and right M-module

    • D. 

      Left and right N-module

  • 10. 
    What does R(G) denote?
    • A. 

      Group of modules

    • B. 

      Radius

    • C. 

      Ring

    • D. 

      Group ring

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