Auslander Reiten Theory Quiz

10 Questions

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Auslander Reiten Theory Quiz

Auslander Reiten Theory is a co-work of Maurice Auslander and Idun Reiten in 1975. Their theory studies the representation theory of Artinian rings using the Sequence and quivers techniques. Try this quiz.


Questions and Answers
  • 1. 
    What part of Algebra is the Auslander Reiten Theory categorized?
    • A. 

      Linear

    • B. 

      Quadratic

    • C. 

      Complex

    • D. 

      Abstract

  • 2. 
    What other name is given the Auslander Reiten Sequence?
    • A. 

      Almost split sequence

    • B. 

      Mid-range sequence

    • C. 

      Anticlimax sequence

    • D. 

      Degree Sequence

  • 3. 
    What does the Auslander Reiten quiver have?
    • A. 

      Variance

    • B. 

      Indiscomposability

    • C. 

      Degree

    • D. 

      Vertex

  • 4. 
    Which of these will warrant adding an arrow in between vertices in an Auslander Reiten quiver?
    • A. 

      When the vertex is negative

    • B. 

      When the sequence is null

    • C. 

      When a morphism is irreducible

    • D. 

      When there is a vector

  • 5. 
    What is the formular of the Auslander Reiten quiver map?
    • A. 

      τ = D Tr ÷∆D

    • B. 

      τ = D Tr

    • C. 

      τ = ∆D Tr

    • D. 

      τ = D.Tr

  • 6. 
    What is another name for the Auslander Reiten quiver map?
    • A. 

      Sequential Transposition

    • B. 

      Translation

    • C. 

      Translocation

    • D. 

      Coordinate

  • 7. 
    What does D stand for in the Auslander Reiten Theory?
    • A. 

      Dual

    • B. 

      Deviation

    • C. 

      Constant Variable

    • D. 

      Domain

  • 8. 
    What does Tr stand for?
    • A. 

      Trigonometric Tripple

    • B. 

      Vector Transpose

    • C. 

      Transpose

    • D. 

      Transpose ratio

  • 9. 
    Which of these satisfies a sequence to be an Auslander Reiten Sequence?
    • A. 

      The sequence is in quadrant

    • B. 

      The sequence is not split

    • C. 

      The sequence is in decreasing order

    • D. 

      The sequence is split

  • 10. 
    Which of these is true for 0→ A → B → C → 0?
    • A. 

      The module B in the almost split sequence is isomorphic to D Tr A

    • B. 

      The module A in the almost split sequence is isomorphic to D Tr C

    • C. 

      The module A in the almost split sequence is interjective to D Tr B

    • D. 

      The module A in the almost split sequence is not isomorphic