Given a ring (R, +, )> an element r R is called idempo- tent when r2

Question:

Given a ring (R, +, •)> an element r ∈ R is called idempo- tent when r2 = r. lf n ∈ Z+ with n > 2, prove that if k ∈ Zn and k is idempotent, then n - k + 1 is idempotent.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jun 21, 2016 09:01 AM

See More Questions

Eq. (12.2.4) is based on the assumption that Z has approximately a normal distribution. Occasionally, the normal approximation is not good enough. In such cases, one can let v = 2/2(1 ). (12.2.6) To...
A number x0 R is called algebraic of degree n if it is the root of a polynomial P(x) = anxn + ............... + a1x + a0, where aj Z, an 0, and n is minimal. A number x0 that is not algebraic is...
If g: Z+ R and c R, we define the function eg: Z+ R by (c(g)(n) = c(g(n)), for each n Z+. Prove that if f, g: Z+ R with f O(g), then f O(cg) for all c R, c 0.
Provide a brief discussion of database connection using the JDBC API, which includes: a. Two popular methods used to establish a connection b. Operational procedure to establish a connection c. How...
1. Based on the information given, summarize the method(s) BMW intends to use for determining incentive pay. Are these rewards for individual, group, and/or company performance? 2. Explain BMWs claim...
In a one-dimensioni random walk, the position x of a walker is computed by: xj = xj + s where s is a random number. Write a program that calculates the number of steps required for the walker to...
An ergodic real-valued random process $U(t)$ with autocorrelation function $\Gamma_{U}(\tau)=\left(N_{0} / 2 ight) \delta(\tau)$ is applied to the input of a linear, time-invariant filter with...
Balance sheet formats The following information is based on the balance sheet of Aracruz Celulose, a Brazilian manufacturer of bleached pulp used to make paper, for the year ended December 31, 2006....
Define temporal accuracy and jitter in RTOS. How does an RTOS manage these factors to ensure predictable and reliable task execution ?
What are some differences between financial and managerial accounting?
For ra, n, r Z+, let p(m, n, r) count the number of partitions of ra into at most n (positive) summands each no larger than r. Evaluate P(k(n + 1), n, n), n Z+. -3
For the hashing function at the end of Example 14.17, find (a) h(123-04-2275); (b) a social security number n such that h(n) = 413, thus causing a collision with the number 081-37- 6495 of the...
What are the major types of costs? Which costs are controllable by the project manager?
Environmental policies have not been changed at the behest of ecoterrorists, nor are concessions typically made to other terrorists or kidnappers. What is the logic behind a policy of noncompliance...
In what situations are command-and-control regulations most appropriate? Provide a specific example that is not from this book.
Consider an electric utility that in 2013 had enough SO 2 allowances to cover its current emissions. If the utility could have reduced its emissions at a cost of $0.15 per ton, should it have done...
The text explains how command-and-control policies, including the Endangered Species Act and the National Pollutant Discharge Elimination System, might be combined with market incentives to yield...
The Endangered Species Act stipulates that recovery plans be established for each listed species without regard to the cost of recovery. Using economic reasoning, explain what you perceive as the...
What are the three functions that every business information system must carry out, irrespective of system architecture?
If the annual fixed costs are 54,000 dinars, the occupation expense represents 20%, the contribution margin is 25%, and the unit selling price is 40 dinars. Required: Calculate the closing point of...
Write the lowest-degree polynomial function that has the given set of zeros and whose graph has the given y-intercept. a. zeros: x = - 4, x = 5, x = - 2 (double root); y-intercept: - 80 b. zeros: x =...
Look back at Exercises 1-4. Find the products of the zeros in Exercise 1. How does the value of the leading coefficient, (, relate to the y-intercept, the product of the zeros, and the degree of the...
Find the missing polynomial in each long-division problem. a. b. x +5)3x + 22x 3Sx 15 7x 38x +15 x + 15 7x2 +35r x+15 0 2x5x3 15x 19x6 15x 10r -3x +6 0
Assume that in Bolivia it takes 9 0 hours of labor to produce a ton of salt and 6 0 hours of labor to produce a ton of soybean oil. In addition, assume that in Brazil it takes 8 0 hours of labor to...
Should governors have centralized power, particularly when dealing with crisis situations? Or should the formal power of the governor remain relatively weak? (You are required to write 100-150 words)
Each scoop of ice cream costs $ 6 . Your benefit associated with each scoop decreases with each additional scoop because you start to get a stomach ache. How many scoops of ice cream should you eat...

Given a ring (R, +, )> an element r R is called idempo- tent when r2

Question:

Step by Step Answer:

n k l 2 k l 2 mod n k 2 ...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Linear Algebra questions