Let S be the ring of all n X n matrices over a division ring D. (a)
Question:
Let S be the ring of all n X n matrices over a division ring D.
(a) S has no proper ideals (that is, 0 is a maximal ideal). 8 or argue directly, using the matrices Er,s mentioned there.]
(b) S has zero divisors. Consequently,
(i) S ≅ S/0 is not a division ring and
(ii) 0 is a prime ideal which does not satisfy condition (1).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 20% (5 reviews)
a Let I be a nonzero ideal of S Then there exists a nonzero matrix A aij I Without loss of ge...View the full answer
Answered By
Morris Maina
I am a professional teaching in different Colleges and university to solved the Assignments and Project . I am Working more then 3 year Online Teaching in Zoom Meet etc. I will provide you the best answer of your Assignments and Project.
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
-
Let : R S be an epimorphism of rings with kernel K. (a) If P is a prime ideal in R that contains K, then f(P) is a prime ideal in S [see Exercise 13]. (b) If Q is a prime ideal in S, then -1 ( Q)...
-
Let R be a ring with identity and S the ring of all n X n matrices over R. J is an ideal of S if and only if J is the ring of all n X n matrices over I for some ideal I in R.
-
(a) The center of the ring S of all 2 X 2 matrices over a field F consists of all matrices of the form (b) The center of Sis not an ideal in S. (c) What is the center of the ring of all n X n...
-
A railroad flatcar is traveling to the right at a speed of 13.0 m/s relative to an observer standing on the ground. Someone is riding a motor scooter on the flatcar (Fig. 3.43). What is the velocity...
-
Professor Kangoh Lee asks his students at Towson State University, "Suppose that in an economy, real consumption, real investment, and real government purchases remain the same from one year to...
-
The costs of energy consumed in producing good units in the Baking Department were $162,000 and $160,000 for August and September, respectively. The number of quivalent units produced in August and...
-
Given the following information, would your decision be to reject or fail to reject the null hypothesis? (Set the level of significance at .05 for decision making.) Provide an explanation for your...
-
Bryant Co. reports the following information for 2012: sales revenue $750,000; cost of goods sold $500,000; operating expenses $80,000; and an unrealized holding loss on available-for-sale securities...
-
Let's keep the focus on the question of monopolies and leveraging monopoly power. Most industries are in a market structure akin to monopolistic competition. We like to explore the extremes of...
-
If you construct a bond portfolio with five 6% coupon (semiannual payment), duration of 2.79 years, 3-year maturity bond sells at par ($1,000) and six 1-year zero coupon bond sells for $950. (a)...
-
If R = Z, A 1 = (6) and A 2 = (4), then the map : R/ A 1 A 2 R/ A 1 X R/ A 2 of Corollary 2.27 is not surjective.
-
Let R be a commutative ring with identity, I an ideal of R and : R R/ I the canonical projection. (a) If S is a multiplicative subset of R, then S = (S) is a multiplicative subset of R/ I. (b) The...
-
An investor purchased Call X and Call Y for a certain stock today, with strike prices 50 and 60, respectively. Both options are European options with the same time to expiration. Determine which of...
-
List three main reasons why governments exist.
-
What barriers to entry exist in the cable television market? Are high cable prices evidence of monopoly power? The Federal Communications Commission (FCC) will make it easier for independent...
-
How does advertising influence demand?
-
Explain the effect of a fall in the oil price on the market for ethanol. If the price of oil remains low for some years, what will be the long-run effects on the market for ethanol and the number of...
-
If in the long run, the market demand for paper remains the same as in Problem 8, a. What is the long-run equilibrium price of paper, the market output, and the economic profit or loss of each firm?...
-
Use two values of R to determine the ratio between an atmosphere and a torr. Does the number make sense?
-
H Corporation has a bond outstanding. It has a coupon rate of 8 percent and a $1000 par value. The bond has 6 years left to maturity but could be called after three years for $1000 plus a call...
-
Suppose that four cases are observed over 1 year among 300 girls 04 years of age with smoking mothers. Answer Problem 7.17 based on these data? Pulmonary Disease Suppose the annual incidence of...
-
What is the SMR for this group? Occupational Health The mortality experience of 8146 male employees of a research, engineering, and metal-fabrication plant in Tonawanda, New York, was studied from...
-
Perform a significance test to assess whether there is an association between long duration of employment and mortality from cirrhosis of the liver in the group hired prior to 1946. Report a p-value?...
-
Suppose the following information is available for Callaway Golf Company for the years 2025 and 2024. (Dollars are in thousands, except share information.) 2025 2024 Net sales $ 1,118,000 $1,125,100...
-
17-20) A company manufactures and sells two types of gloves-Wet Days (WD) and Cold Days (CD)-forurens Current financial data is provided below: Selling Price per pair VC per pair WD CD $8.00 $12.00...
-
Current Attempt in Progress Tamarisk Company traded a used welding machine (cost $11,880, accumulated depreciation $3,960) for office equipment with an estimated fair value of $6,600. Tamarisk also...
Study smarter with the SolutionInn App