Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. for p a given prime number, define the p-adic norm

For p a given prime number, define the p-adic norm | * |p as follows on...

90.2K

Verified Solution

Question

Advance Math

For p a given prime number, define the p-adic norm | * |p asfollows on Q: Given q in Q, we can write it as a product q =(p^m)(a/b) with a,b integers which are not divisible by p, and m aninteger which is uniquely determined by q (check that m is indeeduniquely determined by q). Then define |q|p = p^(-m).

Check that Q with distance dp(q1,q2) = |q1 - q2|p is a metricspace (here q1-q2 just means the usual operation of subtraction inQ). Show moreover
that |q1 + q2|p <= max(|q1|p, |q2|p).

Answer & Explanation Solved by verified expert
3.6 Ratings (336 Votes)
first to see    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

Chemistry
1.2K views

Calculate the standard heat of reaction for the dehydrogenation of cyclohexane to benzene in the vapor...

Biology
1.2K views

please answer these questions all of them for quick 1.  Pick two organisms that have traits that...

Mechanical Engineering
1.2K views

Discuss three (3) key elements of Design for Manufacture (DFM). Elaborate for each of them.

Accounting
1.2K views

The summarized statement of financial positions of A Ltd and B Ltd as at 31 December...

Algebra
1.2K views

Solve for x x3 3 2x 2x 8x 0 x 4 Enter the smallest answer...

Accounting
1.2K views

Marios Marketing Firm, a market research firm, had the following transactions in June, its first...

Accounting
1.2K views

The term Kakure Krishitan refers to what socio/religious phenomena in Japan? Loosening of isolationist policies...

Accounting
1.2K views

Recent reseatch inte the cost of valious miedicol procedures hos shown the impact of certain...

Accounting
1.2K views

Tidex Company is a manufacturer of cleaning detergent. Cleanx is manufactured on a weekly basis....

Accounting
1.2K views

Toys-4-U manufactures a toy that it sells for $30 each. The variable cost per toy...

Accounting
1.2K views

Selected income statement and balance sheet data from Merck & Co. for Year 5 are...

Accounting
1.2K views

Tobin's Barbeque has a bank loan at 9% interest and an after-tax cost of debt...