J(Mat n R} = Mat n J(R). Here is an outline of a proof: (a) If A
Question:
J(MatnR} = MatnJ(R). Here is an outline of a proof:
(a) If A is a left R-module, consider the elements of An = A ⊕ A ⊕· · · ⊕ A (n summands) as column vectors; then An is a left (MatnR)-module (under ordinary matrix multiplication).
(b) If A is a simple R-module, An is a simple (MatnR)-module.
(c) J(MatnR) ⊂ MatnJ(R).
(d) MatnJ(R) ⊂ J(MatnR).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (2 reviews)
To prove that JMatnR MatnJR we need to show both inclusions JMatnR MatnJR This means every element of JMatnR is also an element of MatnJR MatnJR JMatnR This means every element of MatnJR is also an el...View the full answer
Answered By
Aketch Cindy Sunday
I am a certified tutor with over two years of experience tutoring . I have a passion for helping students learn and grow, and I firmly believe that every student has the potential to be successful. I have a wide range of experience working with students of all ages and abilities, and I am confident that I can help students succeed in school.
I have experience working with students who have a wide range of abilities. I have also worked with gifted and talented students, and I am familiar with a variety of enrichment and acceleration strategies.
I am a patient and supportive tutor who is dedicated to helping my students reach their full potential. Thank you for your time and consideration.
0.00
0 Reviews
10+ Question Solved
Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
Question Posted:
Students also viewed these Mathematics questions
-
(a) Reflect pentagon ABCDE, shown below, about line l. Label the reflected pentagon A'B'C'D'E'. (b) Other than vertex labels, is the position of pentagon A'B'C'D'E' identical to the position of...
-
A finite division ring Dis a field. Here is an outline of the proof (in which E* denotes the multiplicative group of nonzero elements of a division ring E). (a) The center K of Dis a field and D is a...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in...
-
A. Hall Company has the following merchandise account balances: Sales Revenue $180,000, Sales Discounts $2,000, Purchases $120,000, and Purchases Returns and Allowances $30,000. In addition, it has a...
-
What is the diference between brainstorming and consensus building?
-
What are three sources of tax assistance?
-
Savallas Company is highly automated and uses computers to control manufacturing operations. The company uses a job-order costing system and applies manufacturing overhead cost to products on the...
-
166. Cooper Company, a retailer of camping supplies has budgeted activity for January using the following data: January cash sales $ 50,000 January credit Sales 380,000 Collections from December...
-
(a) Let I be a nonzero ideal of R[x] and p(x) a nonzero polynomial of least degree in I with leading coefficient a. If (x) R[x] and a m (x) = 0, then a m-1 p(x}f(x} = 0. (b) If a ring R has no...
-
Let R be a ring without identity. Embed Rina ring S with identity which has characteristic zero. Prove that J(R) = J(S). Consequently every semi simple ring may be embedded in a semi simple ring with...
-
For nitrogen gas, c = 740 J/kg K. Assuming it to behave like an ideal gas, find its specific heat at constant pressure. (The molecular mass of nitrogen gas is 28.0 kg/kmol.)
-
How might a qualitative researcher determine an appropriate sample size, and how does this impact transferability? How might a researcher address issues of confidentiality in qualitative research?
-
I need assistance in generating a pop-up display for the pythonOut text file, since it consistently denies access. C VOA + : (D) >_ Python Console x 99 PyDev console: starting. Python 3.10.4...
-
Fill in the chart and answer questions: Cost of Goods Sold Cash Depreciation Interest Expense Selling Expenses Accounts Payable Net Fixed Assets Sales Accounts Receivable Notes Payable Long term...
-
Current year (end of year) 0 Real risk-free rate 2.5% Expected inflation Year 1 8.0% 2 6.0% 3 4.0% 4 3.0% 5 5.0% 6 and beyond 3.0% Maturity risk premium Annual 0.1% Maximum 2.0% Years Real risk-free...
-
How can organizations design marketing communication programs that keep pace with the rapid changes in technology? Provide two examples and explain how these methods will allow organizations to...
-
Skyscraper City has a subway system, for which a one-way fare is $1.50. There is pressure on the mayor to reduce the fare by one-third, to $1.00. The mayor is dismayed, thinking that this will mean...
-
The age-old saying for investing is "buy low and sell high," but this is easier said than done. Investors who panic about falling prices sell their investments, which in turn lowers the price and...
-
What is the estimated rate ratio for colon cancer between the ASA and placebo groups? Cancer Suppose we wish to study the association between aspirin intake and the incidence of colon cancer. We find...
-
Is there a significant difference between these incidence rates? Report a p-value (two-tailed)? Cancer Suppose we wish to study the association between aspirin intake and the incidence of colon...
-
Answer Problem 14.40 under this definition of success? To reduce variability, the investigators also considered a criterion of at least 50% improvement on two successive visits as a definition of...
-
The difference between net sales and cost of goods sold is called (a) gross profit. (b) net purchases. (c) goods available for sale. (d) the bottom line.
-
Soru 4 L-1 e-5s (s - 36) *s) A hibiri =? u(t-5)*[((e^(30-6t))/72) + ((e^(6t-30))/72) - 1/36] Cu(t-5)*[((e^(25-t))/34) + (2*(e^(t-5))/27) - 7/3] BCD Du(t-5)*[((e^(3-4t))/6) + ((e^(2t-3))/12) - 1/6] E...
-
Question 14 Isn convergent or divergent? convergent divergent Question 15 Why is the series in the previous problem convergent or divergent? Upload Choose a File Question 16 en Is convergent or...
Study smarter with the SolutionInn App