Abstract Algebra - Fields

1

What definition does the following correlate to?

If is a prime, then the following polynomial is irreducible over the field of rational numbers.

$\phi(x)=x^{p-1}+...+x+1$

2

What definition does the following correlate to?

If is a prime, then the following polynomial is irreducible over the field of rational numbers.

$\phi(x)=x^{p-1}+...+x+1$

3

Identify the following definition.

Given that lives in the Euclidean plane $\mathbb{R}^2$ . Elements , , and in the subfield that form a straight line who's equation form is , is known as a__________.

4

Identify the following definition.

Given that lives in the Euclidean plane $\mathbb{R}^2$ . Elements , , and in the subfield that form a straight line who's equation form is , is known as a__________.

5

Identify the following definition.

Given that lives in the Euclidean plane $\mathbb{R}^2$ . Elements , , and in the subfield that form a straight line who's equation form is , is known as a__________.

6

Identify the following definition.

Given that lives in the Euclidean plane $\mathbb{R}^2$ . Elements , , and in the subfield that form a straight line who's equation form is , is known as a__________.

7

Identify the following definition.

For some subfield of $\mathbb{R}$ , in the Euclidean plane $\mathbb{R}^2$ , the set of all points that belong to that said subfield is called the __________.

8

Identify the following definition.

For some subfield of $\mathbb{R}$ , in the Euclidean plane $\mathbb{R}^2$ , the set of all points that belong to that said subfield is called the __________.

9

Identify the following definition.

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

10

Identify the following definition.

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

Fields

Practice Questions