Auslander Reiten Theory Quiz
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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.
- 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
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