Let R be a commutative ring with unity u. a) For any (fixed) a R, prove
Question:
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.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 73% (15 reviews)
a a au aR so aR If ar 1 ar 2 aR then ar 1 ar 2 ar 1 ...View the full answer
Answered By
Aysha Ali
my name is ayesha ali. i have done my matriculation in science topics with a+ . then i got admission in the field of computer science and technology in punjab college, lahore. i have passed my final examination of college with a+ also. after that, i got admission in the biggest university of pakistan which is university of the punjab. i am studying business and information technology in my university. i always stand first in my class. i am very brilliant client. my experts always appreciate my work. my projects are very popular in my university because i always complete my work with extreme devotion. i have a great knowledge about all major science topics. science topics always remain my favorite topics. i am also a home expert. i teach many clients at my home ranging from pre-school level to university level. my clients always show excellent result. i am expert in writing essays, reports, speeches, researches and all type of projects. i also have a vast knowledge about business, marketing, cost accounting and finance. i am also expert in making presentations on powerpoint and microsoft word. if you need any sort of help in any topic, please dont hesitate to consult with me. i will provide you the best work at a very reasonable price. i am quality oriented and i have 5 year experience in the following field.
matriculation in science topics; inter in computer science; bachelors in business and information technology
_embed src=http://www.clocklink.com/clocks/0018-orange.swf?timezone=usa_albany& width=200 height=200 wmode=transparent type=application/x-shockwave-flash_
4.40+
11+ Reviews
14+ 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, and let I be an ideal of R. (a) If u 1, prove that I = R. (b) If I contains a unit of R, prove that I = R.
-
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)...
-
Midge is a 10% limited partner in Wild Catter, an oil and gas drilling partnership. She received her partnership interest in exchange for a $10,000 investment in the partnership. The balance in her...
-
What types of databases might be found in the following organizations? a. Holiday Inn b. A major universitys athletic department c. Anheuser-Busch
-
A population has mean = 7 and standard deviation = 2. a. Find the z-score for a population value of 5. b. Find the z-score for a population value of 10. c. What number has a z-score of 2?
-
\(n_{1}\) moles of an ideal monoatomic gas at temperature \(T_{1}\) and pressure \(P\) are in one compartment of an, insulated container. In an adjoining compartment, separated by an insulating...
-
Calculating Ending Inventory and Cost of Goods Sold Under FIFO, LIFO, and Average Cost Hamilton Company uses a periodic inventory system. At the end of the annual accounting period, December 31,...
-
The following data, expressed as $10 4 , are the closed ledger accounts showing assets, liabilities, income, and expenses of Blue River Fabricators, Inc., a family owned firm that does not declare...
-
For the cache design of the preceding problem, suppose that increasing the line size from one word to four words results in a decrease of the read miss rate from 3.2% to 1.1%. For both the non burst...
-
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....
-
Let (S, +, ) and (T, +', ') be two rings. For R = S T, define addition "" and multiplication "" by (s1, t1) (s2, t2) = (S1 + S2, t1 +' t2), (s1 t1) (s2, t2) = (S1 s2, t1. t2). (a) Prove that...
-
In Exercises 35 and 36, use a computer algebra system to evaluate c F dr. F(x, y, z) = xzi + 6yj + yzk C: r(t) = ti + tj + In tk, 1 t 3
-
What do the marketing people do at this company? Do they work with an advertising agency? If so, how do they interact? If they dont work in an advertising agency, do they have an in-house agency? If...
-
How would you describe yourself as a writer? What do you believe are some characteristics or qualities you possess that will assist you with the writing you will do in your career?
-
Consider the metric \[ d s^{2}=\frac{R^{2}}{ho^{2}+R^{2}} d ho^{2}+ho^{2} d \theta^{2}+ho^{2} \sin ^{2} \theta d \phi^{2} \] where \(R\) is a positive characteristic length. Notice that one considers...
-
Often, applying for jobs with organizations that have a global presence can be more competitive than job roles in domestic organizations. The requirements of global employers may be broader and...
-
Innovative Consulting Co. has the following accounts in its ledger: Cash, Accounts Receivable, Supplies, Office Equipment, Accounts Payable, Common Stock, Retained Earnings, Dividends, Fees Earned,...
-
Kent Duncan is exploring the possibility of opening a self-service car wash and operating it for the next five years until he retires. He has gathered the following information: a. A building in...
-
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...
-
The International Canine Academy raises and trains Siberian sled dogs and dancing French poodles. Breeders can supply the academy with at most 20 poodles and 15 Siberian huskies each year. Each...
-
The Elite Pottery Shoppe budgets a maximum of $1,000 per month for newspaper and radio advertising. The newspaper charges $50 per ad and requires at least four ads per month. The radio station...
-
A small electric generating plant must decide how much low-sulfur (2%) and high-sulfur (6%) oil to buy. The final mixture must have a sulfur content of no more than 4%. At least 1200 barrels of oil...
-
You will make a post giving your point-of-view (PoV) on a brand's activities and/or marketing campaign. Give your PoV on what brands can and should do to ensure they are creating a great digital...
-
IM.83 A distribution center for a sporting goods retailer places orders with manufacturers for a variety of items. Among these is a popular standard skateboard, targeted to first-time skate boarders....
-
[5] 5. Determine the area of the shaded region, if the radius of each circle is 5 cm.
Study smarter with the SolutionInn App