Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. theorem: let k/f be a field extension and let a ?

Theorem: Let K/F be a field extension and let a ? K be algebraic over F....

80.2K

Verified Solution

Question

Advance Math

Theorem: Let K/F be a field extension and let a ? K be algebraicover F. If deg(mF,a(x)) = n, then

1. F[a] = F(a).

2. [F(a) : F] = n, and

3. {1, a, a2 , ..., an?1} is a basis for F(a).

Answer & Explanation Solved by verified expert
4.3 Ratings (876 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

Explain in detail the mechanisms of fluid exchange between capillaries and the interstitium. Then, define edema, and...

Medical Sciences
Q

In a typical single twitch of a muscle, when exactly does cross-bridge cycling begin?When calcium...

Biology
Q

The cylinder below has a radius of 6 m and a height of 15 m...

Geometry
Q

Consider two displacement vectors defined by their magnitudes and directions as follows A has a...

Geometry
Q

Which choice is equivalent to log73m 2x A 282x 12m B 288x 48m 4 7...

Basic Math
Q

y

Calculus
Q

hemist has a 100 gram sample of a radioactive material He records the amount of...

Algebra
Q

image
image
image
image

Accounting
Q

1. Identify which accounts are affected in each transaction. Keep in mind that every transaction...

Accounting
Q

A company wants to evaluate the effects of a reduction in material cost of 2%...

Accounting
Q

Question 2[6 points] NorthCo manufactures a powerful cleaning solvent. The main ingredient in the...

Accounting
Q

There are three fundamental limitations on the qualified business income deduction. An overall limitation (based...

Accounting