Abstract Algebra : Geometric Fields

Study concepts, example questions & explanations for Abstract Algebra

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Example Questions

Example Question #2 : Fields

Identify the following definition.

For some subfield of , in the Euclidean plane , the set of all points  that belong to that said subfield is called the __________.

Possible Answers:

Constructible Line

Line

Angle

Plane

None of the answers.

Correct answer:

Plane

Explanation:

By definition, when  is a subfield of , in the Euclidean plane , the set of all points  that belong to  is called the plane of .

Example Question #3 : Fields

Identify the following definition.

Given that  lives in the Euclidean plane . Elements , and  in the subfield  that form a straight line who's equation form is , is known as a__________.

Possible Answers:

Plane

Circle in 

Line in 

Angle

Subfield

Correct answer:

Line in 

Explanation:

By definition, given that  lives in the Euclidean plane . When elements , and  in the subfield  , form a straight line who's equation form is , is known as a line in .

Example Question #4 : Fields

Identify the following definition.

Given that  lives in the Euclidean plane . Elements , and  in the subfield  that form a straight line who's equation form is , is known as a__________.

Possible Answers:

Subfield

Circle in 

Plane

Angle

Line in 

Correct answer:

Line in 

Explanation:

By definition, given that  lives in the Euclidean plane . When elements , and  in the subfield  , form a straight line who's equation form is , is known as a line in .

Example Question #5 : Fields

Identify the following definition.

If a line segment has length  and is constructed using a straightedge and compass, then the real number  is a __________.

Possible Answers:

Magnitude

Constructible Number 

Straight Line

Angle

Plane

Correct answer:

Constructible Number 

Explanation:

By definition if a line segment has length  and it is constructed using a straightedge and compass then the real number  is a known as a constructible number.

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