Auslander Algebra Trivia Quiz
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Which of these is a summed up module of Algebra A?
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Integrated modules
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Indecomposable module
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Projective module
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Isomorphic module
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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.
Quiz Preview
- 2.
When did Auslander introduce the Algebra?
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1874
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1870
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1974
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1989
Correct Answer
A. 1974 -
- 3.
In these fomular, k[T ]=hT n i, what does k stand for?
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Term
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Natural value
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Module
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Field
Correct Answer
A. FieldExplanation
The correct answer is "Field". In the given formula, k represents the field. A field is a mathematical structure that consists of a set of elements along with operations such as addition and multiplication. In this context, k is the field used to represent the relationship between temperature (T) and the rate constant (k) in a chemical reaction.Rate this question:
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- 4.
What kind of ring is the sum of indecomposable module of A in the Auslander Algebra?
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Module
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Endomorphism
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Homomorphism
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Artin
Correct Answer
A. EndomorphismExplanation
The sum of indecomposable modules of A in the Auslander Algebra is an endomorphism. This means that it is a module that is both a domain and a codomain of a homomorphism, and the homomorphism is from the module to itself. In other words, it represents the set of all possible mappings from the module to itself.Rate this question:
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- 5.
Which of these satisfies the condition for an Artin Algebra to be an Auslander Algebra?
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Γ ≤ 2
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Γ ≥ 2
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Γ < 1
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Γ > 2
Correct Answer
A. Γ ≤ 2Explanation
An Artin Algebra is an Auslander Algebra if its global dimension (Γ) is less than or equal to 2. This means that the algebra has a finite projective resolution of length 2 or less.Rate this question:
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- 6.
Which of these people is connected to the Auslander Algebra?
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Reinten
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Becleau
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Herin
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Phills
Correct Answer
A. ReintenExplanation
Reinten is connected to the Auslander Algebra.Rate this question:
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- 7.
Which of these explains Auslander Algebra of any representation of finite Algebra?
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Budding of Fl
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Blossom of flowers
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Quasi Hereditary
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Passing of Gene
Correct Answer
A. Quasi HereditaryExplanation
Quasi Hereditary is an explanation for the Auslander Algebra of any representation of a finite Algebra. Quasi Hereditary refers to a property of certain categories that allows for the decomposition of modules into a direct sum of indecomposable modules. This property is closely related to the Auslander-Reiten theory, which studies the structure of modules and their relations in a given algebra. Therefore, the concept of Quasi Hereditary provides a valid explanation for the Auslander Algebra of any representation of a finite Algebra.Rate this question:
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- 8.
What does T represent in the Auslander formular?
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Constant
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Value for Artin constant
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Variable
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Function
Correct Answer
A. VariableExplanation
The correct answer is "Variable." In the Auslander formula, T represents a variable. This means that its value can change and is not fixed.Rate this question:
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- 9.
What does the n in the Auslander formular stand for?
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Integers
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Natural Number
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Rational number
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Constant
Correct Answer
A. Natural NumberExplanation
The "n" in the Auslander formula stands for natural number. A natural number is a positive integer greater than zero that is used to count or label objects. In the context of the Auslander formula, it is likely used as a parameter or variable representing a specific natural number value.Rate this question:
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- 10.
Which of these symbol represents Artin Algebra in relation to Auslander Algebra?
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∆
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μ
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Λ
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Γ
Correct Answer
A. ΓExplanation
The symbol Γ represents Artin Algebra in relation to Auslander Algebra. This is because Γ is commonly used to denote the Auslander-Reiten quiver, which is a directed graph that represents the indecomposable modules of an Artin algebra. The Auslander-Reiten quiver provides important information about the structure and representation theory of the Artin algebra, making Γ the correct symbol to represent it.Rate this question:
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![In these fomular, k[T ]=hT n i, what does k stand for? - ProProfs](https://media.proprofs.com/images/QM/user_images/2305925/1554960814.png "In these fomular, k[T ]=hT n i, what does k stand for?")
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Current Version
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Mar 18, 2023Quiz Edited by
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Apr 09, 2019Quiz Created by
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