Let R be a commutative ring with unity u, and let I be an ideal of R.
Question:
(a) If u ∈ 1, prove that I = R.
(b) If I contains a unit of R, prove that I = R.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 71% (7 reviews)
a I R For each r B ru r I so R I ...View the full answer
Answered By
Mishark muli
Having any assignments and any other research related work? worry less for I am ready to help you with any task. I am quality oriented and dedicated always to produce good and presentable work for the client once he/she entrusts me with their work. i guarantee also non plagiarized work and well researched work to give you straight As in all your units.Feel free to consult me for any help and you will never regret
4.70+
11+ Reviews
37+ Question Solved
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Question Posted:
Students also viewed these Linear Algebra questions
-
Let R be a commutative ring with unity u. a) For any (fixed) a R, prove that aR = {ar| r R] is an ideal of R. b) If the only ideals of R are {z} and R, prove that R is a field.
-
Let A = R+. Define and on A by a b = ab, the ordinary product of a, b; and a b = alog2b. (a) Verify that (A, , ) is a commutative ring with unity. (b) Is this ring an integral domain or field?
-
(a) Let (R, +, ) be a finite commutative ring with unity u. If r R and r is not the zero element of R, prove that r is either a unit or a proper divisor of zero. (b) Does the result in part (a)...
-
Dale and Roy formed a partnership early this year. Dale contributed $150,000 cash in exchange for a 50% interest in the partnership. Roy contributed land with a tax basis of $90,000, and a fair...
-
What makes a decision support system successful?
-
Elaina Company has the following investment as of December 31, 2022: Investment in debt securities of FourSquare Company ...... $3,300,000 The carrying value and the fair value of the investment are...
-
What are some constraints in user interface design?
-
Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height h, as...
-
Explain the type of electromagnetic spectrum and how the electromagnetic spectrum is used of visible light, radio waves, microwaves, infrared radiation, ultraviolet radiation, and x-rays and gamma...
-
Ashley attended an in-service education program about the outpatient prospective payment system (OPPS) where she learned that certain Medicare Part B services are paid according to ambulatory payment...
-
Let (R, +, ) be a commutative ring, and let z denote the zero element of R. For a fixed element a R, define N(a) = [r R | ra = z}. Prove that N(a) is an ideal of R.
-
Let (R, +, ) be the (finite) commutative ring with unity given by Tables 14.6(a) and (b). (a) Verify that R is a field. (b) Find a subring of R that is not an ideal. (c) Let x and y be unknowns....
-
A rocket propellant manufacturer is studying the burning rate of propellant from three production processes. Four batches of propellant are randomly selected from the output of each process and three...
-
During this experiment, a metal will be placed in fire and an electron will absorb enough energy to be promoted to a higher energy state. What do we call this higher energy state?
-
A boat attempts to cross a river by traveling [W] at 9.85 m/s. If there is a current travelling [E] at 2.83 m/s and the river is 70.2 m wide, determine the time it takes the boat to cross
-
The Santa Cruz River is about 600 ft in the Sunset Road reach. The channel slope is 0.3%, and Manning's roughness coefficient is 0.06. The design flow discharge is 70,000 cfs. For the proposed sunset...
-
You are on a strange new planet and you measure a weight of 2.2 Newtons acting on a 2 kg block. What is the gravitational acceleration of the planet
-
Clark was driving his four-wheeler 15 meters per second on a dirt road. It had just rained and there were massive mud puddles on the road. He hits on and it slows him to a speed of 3.7 meters per...
-
What is value-based customer segmentation? Why is it used?
-
The Place-Plus real estate development firm in Problem 24 is dissatisfied with the economists estimate of the probabilities of future interest rate movement, so it is considering having a financial...
-
Consider this system of equations: a. Write the augmented matrix for this system. 5x-2y +5 = 0
-
Find the equation of the parabola at right? 0.-15 2-2.5) +4+4
-
For the system in Exercise 1, find the vertex that optimizes these expressions: a. maximize: 5x + 2y b. minimize: x + 3y c. maximize: x + 4y d. minimize: 5x + y e. What generalizations can you make...
-
Write the feature of Super's Career Development Assessment and Counseling (C-DAC) system?
-
Describe one type of role-play technique you could use in a specific group setting. Explain who would benefit from this technique and why. Toseland, R. W., & Rivas, R. F. (2017). An introduction to...
-
Suppose that a manager is following a base stock policy where the optimal inventory position is 10. Assume the component lead time is 2 days. At the end of day 1, there is no ordered units yet to be...
Study smarter with the SolutionInn App