# Auslander Algebra Trivia Quiz

Approved & Edited by ProProfs Editorial Team
The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.
| By Gregorynaomi
G
Gregorynaomi
Community Contributor
Quizzes Created: 1463 | Total Attempts: 756,371
Questions: 10 | Attempts: 134

Settings

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.

• 1.

### Which of these is a summed up module of Algebra A?

• A.

Integrated modules

• B.

Indecomposable module

• C.

Projective module

• D.

Isomorphic module

B. Indecomposable module
Explanation
An indecomposable module is a module that cannot be expressed as the direct sum of two non-zero submodules. In other words, it cannot be "broken down" into smaller modules. This makes it a summed up module of Algebra A because it represents a fundamental building block that cannot be further simplified or decomposed.

Rate this question:

• 2.

• A.

1874

• B.

1870

• C.

1974

• D.

1989

C. 1974
• 3.

### In these fomular, k[T ]=hT n i, what does k stand for?

• A.

Term

• B.

Natural value

• C.

Module

• D.

Field

D. Field
Explanation
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:

• 4.

### What does T represent in the Auslander formular?

• A.

Constant

• B.

Value for Artin constant

• C.

Variable

• D.

Function

C. Variable
Explanation
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:

• 5.

### What does the n in the Auslander formular stand for?

• A.

Integers

• B.

Natural Number

• C.

Rational number

• D.

Constant

B. Natural Number
Explanation
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:

• 6.

### Which of these symbol represents Artin Algebra in relation to Auslander Algebra?

• A.

• B.

μ

• C.

Λ

• D.

Γ

D. Γ
Explanation
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:

• 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

B. Endomorphism
Explanation
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:

• 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

A. Γ ≤ 2
Explanation
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:

• 9.

### Which of these people is connected to the Auslander Algebra?

• A.

Reinten

• B.

Becleau

• C.

Herin

• D.

Phills

A. Reinten
Explanation
Reinten is connected to the Auslander Algebra.

Rate this question:

• 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

C. Quasi Hereditary
Explanation
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:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

• Current Version
• Mar 18, 2023
Quiz Edited by
ProProfs Editorial Team
• Apr 09, 2019
Quiz Created by
Gregorynaomi

Related Topics