Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. a ?eld f is said to be perfect if every polynomial

A ?eld F is said to be perfect if every polynomial over F is separable. Equivalently, every...

80.2K

Verified Solution

Question

Advance Math

A ?eld F is said to be perfect if every polynomialover F is separable. Equivalently,
every algebraic extension of F is separable. Thus ?elds ofcharacteristic zero and
?nite ?elds are perfect. Show that if F has prime characteristic p,then F is perfect
if and only if every element of F is the pth power of some elementof F. For short we
write F = F p.

Answer & Explanation Solved by verified expert
3.5 Ratings (475 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

Accounting
1.2K views

John’s Custom Computer Shop (JCCS) assembles computers for bothindividual and corporate customers. The company...

Statistics
1.2K views

Consider the class average in an exam in a few different settings. In all cases, assume...

Chemistry
1.2K views

Discuss the use of Lanthanide shift reagents (LSR) in NMR spectroscopy, both how it works and...

Programming
1.2K views

A Private Poly Clinic in Oman wish to develop software to automate their Patient Monitoring system...

Advance Math
1.2K views

Use LP Formulation to find the best alternative to the situation below. “Show & Sell” can advertise...

Physics
1.2K views

A rectangular a square a circular and an elliptical loop all in the x y...

Basic Math
1.2K views

i need help with determining the formula to get the values for x and y...

Calculus
1.2K views

Let f x 1 8x x x Find the derivative by using the Product Rule...

Accounting
1.2K views

Palm Beach Hotel accepts telephone reservations for rooms during its summer tourist season, but requires...

Accounting
1.2K views

what are your thoughts in regards to crypto currency in terms of the three "des"...

Finance
1.2K views

Quantitative Problem: Rosnan Industries' 2019 and 2018 balance sheets and income statements are shown below....

Accounting
1.2K views

S2 Ltd s $ Extracts from the group's statements of financial position as at 31...