Auslander Algebra Trivia Quiz

10 Questions | Total Attempts: 100

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Auslander Algebra Trivia Quiz

The Auslander Algebra is a work of Maurice Auslander a famous American Mathematician. His work was an Artin Algebra representation. An Artin Algebra is an Auslander Algebra if gl dim Γ ≤ 2 and if 0→Γ→I→J→K→0 is a minimal injective resolution of Γ then I and J are projective Γ-modules; where Γ is the Artin Algebra. Try out this quiz.


Questions and Answers
  • 1. 
    Which of these is a summed up module of Algebra A?
    • A. 

      Integrated modules

    • B. 

      Indecomposable module

    • C. 

      Projective module

    • D. 

      Isomorphic module

  • 2. 
    When did Auslander introduce the Algebra?
    • A. 

      1874

    • B. 

      1870

    • C. 

      1974

    • D. 

      1989

  • 3. 
    In these fomular, k[T ]=hT n i, what does k stand for?
    • A. 

      Term

    • B. 

      Natural value

    • C. 

      Module

    • D. 

      Field

  • 4. 
    What does T represent in the Auslander formular?
    • A. 

      Constant

    • B. 

      Value for Artin constant

    • C. 

      Variable

    • D. 

      Function

  • 5. 
    What does the n in the Auslander formular stand for?
    • A. 

      Integers

    • B. 

      Natural Number

    • C. 

      Rational number

    • D. 

      Constant

  • 6. 
    Which of these symbol represents Artin Algebra in relation to Auslander Algebra?
    • A. 

    • B. 

      μ

    • C. 

      Λ

    • D. 

      Γ

  • 7. 
    What kind of ring is the sum of indecomposable module of A in the Auslander Algebra?
    • A. 

      Module

    • B. 

      Endomorphism

    • C. 

      Homomorphism

    • D. 

      Artin

  • 8. 
    Which of these satisfies the condition for an Artin Algebra to be an Auslander Algebra?
    • A. 

      Γ ≤ 2

    • B. 

      Γ ≥ 2

    • C. 

      Γ < 1

    • D. 

      Γ > 2

  • 9. 
    Which of these people is connected to the Auslander Algebra?
    • A. 

      Reinten

    • B. 

      Becleau

    • C. 

      Herin

    • D. 

      Phills

  • 10. 
    Which of these explains Auslander Algebra of any representation of finite Algebra?
    • A. 

      Budding of Fl

    • B. 

      Blossom of flowers

    • C. 

      Quasi Hereditary

    • D. 

      Passing of Gene