# A Practice Quiz About Algebra Representation

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Algebra representation is a branch of algebra in abstract algebra and is described as a representation of an associative algebra. It is true that it sounds more like something that a math geek would know about but if you look closely, most of it is very basic. So, what do you know about this branch of algebra? Take our quiz and find out.

• 1.

### What's a complex structure?

• A.

It's an morphism of V that squares to the minus identity

• B.

It's an metamorphism of V that squares to the minus identity

• C.

It's an automorphism of V that squares to the minus identity

• D.

It's an automorphism of Q that squares to the minus identity

C. It's an automorpHism of V that squares to the minus identity
• 2.

### What's a complex number?

• A.

It's a number that can be expressed in the form of a+bi, where a and b are real numbers.

• B.

It's a number that can be expressed in the form of a+bi, where a is a real number.

• C.

It's a number that can be expressed in the form of a+bi, where b is real number.

• D.

It's a number that can be expressed in the form of a+bi, where a and i are real numbers.

A. It's a number that can be expressed in the form of a+bi, where a and b are real numbers.
Explanation
A complex number is a number that can be expressed in the form of a+bi, where a and b are real numbers. This form includes both a real part (a) and an imaginary part (bi), where i is the imaginary unit. The real part represents the horizontal component of the number on the complex plane, while the imaginary part represents the vertical component. Therefore, a complex number combines both real and imaginary components.

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• 3.

### What's the other term for a polynomial ring?

• A.

Polynomial mathematics

• B.

Polynomial algebra

• C.

Polynomial calculation

• D.

Polynomial circle

B. Polynomial algebra
Explanation
The other term for a polynomial ring is "Polynomial algebra." This term is used to describe the study and manipulation of polynomials, which are mathematical expressions consisting of variables and coefficients combined through addition, subtraction, multiplication, and exponentiation. Polynomial algebra involves various operations and techniques for solving equations and analyzing polynomial functions.

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• 4.

### What's commutative algebra?

• A.

It's the branch of algebra that studies commutative rings.

• B.

It's the branch of algebra that studies commutative rings and their origins.

• C.

It's the branch of geometry that studies commutative rings, their ideals, and modules over such rings.

• D.

It's the branch of algebra that studies commutative rings, their ideals, and modules over such rings.

D. It's the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
Explanation
The correct answer is the last option: "It's the branch of algebra that studies commutative rings, their ideals, and modules over such rings." This answer accurately describes commutative algebra as a branch of algebra that focuses on the study of commutative rings, their ideals, and modules.

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• 5.

### What's algebraic geometry?

• A.

It's a branch of mathematics, classically studying zeros of multivariate polynomials

• B.

It's a branch of mathematics, classically studying ones of multivariate polynomials

• C.

It's a branch of mathematics, classically studying threes of multivariate polynomials

• D.

It's a branch of mathematics, classically studying tens of multivariate polynomials

A. It's a branch of mathematics, classically studying zeros of multivariate polynomials
Explanation
Algebraic geometry is a branch of mathematics that focuses on studying the zeros (also known as solutions or roots) of multivariate polynomials. This field combines techniques from algebra and geometry to understand the geometric properties of these solutions and their relationships. By examining the zeros of polynomials, algebraic geometry provides insights into the structure and behavior of algebraic varieties, which are objects defined by polynomial equations.

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• 6.

### What's triangular matrix?

• A.

It's a special kind of cylindre matrix.

• B.

It's a special kind of circle

• C.

It's a special kind of square matrix.

• D.

It's a special kind of shape matrix.

C. It's a special kind of square matrix.
Explanation
A triangular matrix is a special type of square matrix where all the elements either above or below the main diagonal are zero. In other words, all the elements in the matrix either lie on or below the main diagonal (lower triangular matrix) or on or above the main diagonal (upper triangular matrix). This type of matrix has a distinct shape, resembling a triangle, hence the name "triangular matrix".

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• 7.

### What's the other term for eigen vector?

• A.

Super vector

• B.

One vector

• C.

Characteristic vector

• D.

Old vector

C. Characteristic vector
Explanation
The other term for eigen vector is characteristic vector.

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• 8.

### What's the other term for linear functional?

• A.

Linear oval

• B.

Linear shape

• C.

Linear curve

• D.

Linear form

D. Linear form
Explanation
A linear functional is another term for a linear form. A linear form is a linear mapping from a vector space to its field of scalars. It takes a vector as input and returns a scalar value. Therefore, the correct answer is "Linear form."

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• 9.

### What's derived algebra?

• A.

It's also called algebra g, which is solvable if its derived series terminates in the 0 sub algebra

• B.

It's also called a Lie algebra r, which is solvable if its derived series terminates in the 0 sub algebra

• C.

It's also called a Lie algebra a, which is solvable if its derived series terminates in the 0 sub algebra

• D.

It's also called a Lie algebra g, which is solvable if its derived series terminates in the 0 subalgebra

D. It's also called a Lie algebra g, which is solvable if its derived series terminates in the 0 subalgebra
• 10.

### What's are algebraic varieties?

• A.

They are the central objects of study in algebraic geometry

• B.

They are some of the objects of study in algebraic geometry

• C.

They are the last objects of study in algebraic geometry

• D.

They are the central objects of study in geometry

A. They are the central objects of study in algebraic geometry
Explanation
Algebraic varieties are the central objects of study in algebraic geometry. This field of mathematics focuses on the study of geometric objects defined by polynomial equations. Algebraic varieties are sets of points in affine or projective space that satisfy a system of polynomial equations. They play a fundamental role in algebraic geometry as they provide a way to understand the geometry of these objects through algebraic methods.

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• Current Version
• Mar 18, 2023
Quiz Edited by
ProProfs Editorial Team
• Aug 01, 2018
Quiz Created by
Anouchka

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