Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. let r and s be nontrivial rings (i.e., containing

Let R and S be nontrivial rings (i.e., containing more than just the 0 element), and...

90.2K

Verified Solution

Question

Advance Math

Let R and S be nontrivial rings (i.e., containing more than justthe 0 element), and define the projection homomorphism pi_1: R X S--> R by pi_1(x,y)=x.

(a) Prove that pi_1 is a surjective homomorphism of rings.

(b) Prove that pi_1 is not injective

(c) Prove that (R X S)/R (not congruent) R.

Please show all parts of answer

Answer & Explanation Solved by verified expert
3.7 Ratings (329 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

How do the typical drinking patterns of Jews differ from those of Conservative Protestants (such as...

Psychology
Q

Database System Question An automobile part trading company would like to store the following attributes for each part...

Electrical Engineering
Q

Which of the following is not found in a reducing atmosphere OH2 O NH3 O...

Biology
Q

c d zero 46 In question number 45 what will be the electric field 51...

Physics
Q

Plastic parts produced by an injection molding operation are checked for conformance to specifications Each...

Statistics
Q

Find the value of the property given the following Annual Rent 612Vacancy and collection los...

Algebra
Q

Sales $ 170,000 $ 950,000 $ 58,000 $ 277,000 Sales...

Accounting
Q

The adjusted trial balance of Sunland Company contained the following information: Sales Returns and...

Accounting
Q

(20 pts) Quahog purchased 15% of Clam on January 1,2021 for $340,000 in cash and...

Accounting
Q

Please explain the days sales uncollected ratio and how is it used to assess liquidity.

Accounting
Q

Happy Ten Co produces sports socks. The company has fixed costs of $91,080 and variable...

Accounting
Q

You have the following instruments; please calculate the PV of the following bonds (with face...

Finance