Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. an element a in a ring r is called nilpotent if th

An element a in a ring R is called nilpotent if there exists an n such...

50.1K

Verified Solution

Question

Advance Math

An element a in a ring R is called nilpotent if there exists ann such that an = 0.

(a) Find a non-zero nilpotent element in M2(Z).

(b) Let R be a ring and assume a, b ? R have at = 0and bm = 0 for some positive integers t and m. Find an nso that (a + b)n = 0. (You just need to find any n thatwill work, not the smallest!)

(c) Show that the set of nilpotent elements in a commutativering R forms a subring of R.

(d) Does this subring from the previous question contain aunity?

(e) Are the Gaussian integers from an earlier question anintegral domain? Explain your answer.

Answer & Explanation Solved by verified expert
3.7 Ratings (656 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

Finance
1.2K views

You are given the following information concerning Around Town Tours: Debt: 8,500, 8 percent coupon bonds...

Medical Sciences
1.2K views

1. To which class do collagen fibers belong? ___________________________ 2. What is the monomer for this class...

General Management
1.2K views

Analyze a recent purchase you made of a durable good (durable goods are goods that don't...

Geometry
1.2K views

atch the equation with its graph x 36y2 492 1 DO O DOK

Basic Math
1.2K views

the Venn diagram to determine the set An B COXS

Calculus
1.2K views

Determine the points in the interval 0 2x at which the graph of the function...

Accounting
1.2K views

Q4: ------------ is the exchange rate for immediate delivery of currencies exchanged. Spot rate has...

Accounting
1.2K views

2849 30 \$32000 339000 1341 00a 2849 30 \$32000 339000 1341...

Accounting
1.2K views

Ashley Williams opened Ashleys Maids Cleaning Service on July 1, 2020. During July, the company...

Accounting
1.2K views

Which of the following are not qualifying certifications for Continuing Education Credits? A. Military B....

Accounting
1.2K views

Cul es el costo de los bienes fabricados para 2018? Producto terminado inicial, 1/1/2018 $47...

Accounting
1.2K views

The correct answer is B but I don't know how to get there. Please explain...