If Vis a vector space over a division ring and fa V*, let W = I a

Question:

If Vis a vector space over a division ring and fa V*, let W = I a a V I (a,f) = 0 l, then Wis a subspace of V. If dim V is finite, what is dim W?

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

Step by Step Answer:

Related Book For book-img-for-question

Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

See More Books

Question Posted: Apr 15, 2023 03:04 AM

See More Questions

Let F be an algebraic closure of the field Q of rational numbers and let E F be a splitting field over Q of the set S = { x 2 + a | a Q} so that E is algebraic and Galois over Q (Theorem 3.11). (a)...
Give a one- or two-sentence synopsis of the proof of Theorem 31.4. Data from Theorem 31.4 If E is a finite extension field of a field F, and K is a finite extension field of E, then K is a finite...
Let S be a nonempty subset of a vector space V over a division ring. The annihilator of S is the subset S 0 of V* given by S = { V*| (s,) = 0 for all s S}. (a) 0 = V*; v 0 = O; S {0} =>S 0 V*....
The accompanying table shows data from the World Bank, World Development Indicators, for real GDP per capita (2010 U.S. dollars) in France, Japan, the United Kingdom, and the United States in 1960...
"The Fed should just increase the money supply at the same rate that the full-employment econ omy grows, and the government should desist from any stabilizing urges." What school of thought would...
Prepare the statement of cash flows under the indirect method for the Snail Company using the information from P6- 10 and the following cash flow information: In p6-10 Snal Company Income Statement...
Show that the force acting on a control surface of any arbitrary control volume is equal to the force on a larger regularly shaped control volume enclosing the given body. In order to do this you...
Joan Chris is the Denver district manager of Stale- Mart, an old established chain of more than 100 department stores. Her district contains eight stores in the Denver metropolitan area. One of her...
Please help me solve the error to this Matlab question 2D. Image transcription text Consider a system similar to that considered in Problem 1 but with a different transfer function: V(s) 10 G(s) =...
1. Based on what you read in this chapter, what would you have suggested Lisa and her team do first with respect to training, particularly in terms of the companys strategy? Why? 2. Have Lisa and the...
The usual injection : Z 2 Z 4 is a monomorphism of abelian groups. Show that l :Z 2 Z 2 Z 2 Z 4 d is the zero map (butZ 2 Z 2 O; see Exercise 2). Data from exrecise 2 Let A and B be abelian...
Without using Lemma 3.9 prove that: (a) Every homomorphic image of a divisible abelian group is divisible. (b) Every direct summand of a divisible abelian group is divisible. (c) A direct sum of...
In each Exercise, we have given the P-value for a hypothesis test. For each exercise, refer to Table 9.8 to determine the strength of the evidence against the null hypothesis. P = 0.184 TABLE 9.8...
What is the form of Maxwell's equations in a region of space that does not contain any charged particles?
Five years ago, Jerome bought 100 shares of Kodak at $60 per share. Last month, he sold the 100 shares at $55 per share. Jerome has a capital gain from the sale. True or False
The emitting antenna of a $100-\mathrm{kW}$ radio station radiates equally in all directions. What are the magnitudes $E_{\max }$ and $B_{\max }(a) 100 \mathrm{~m}$ from the antenna and \((b)...
Assume a $60-\mathrm{W}$ incandescent light bulb radiates uniformly in all directions. At a distance of $2.0 \mathrm{~m}$ from the bulb, determine $(a)$ the intensity of the electromagnetic...
For a constant current of $0.20 \mathrm{~A}$, what time interval is required to deliver 1. 0 MW of power to the space between the plates of an initially discharged capacitor if the plates are...
1. Do Jerry and Robert understand what management of diversity means? How would you advise them? 2. Considering the marketing plans, how could they benefit from a more diverse management team? Be...
The company manufactures three products: wooden chairs, tables and dressers. AFC started off as a 'Mom & Pop' shop but has grown rapidly. AFC uses one assembly line to build all three products,...
A survey of 60 individuals leaving a mall asked how many stores they entered during this visit to the mall. The figures are listed here. a. Draw a histogram to summarize these data. b. Describe the...
Among American adults with children draw a histogram of their ages when their first child was born (AGEKDBRN).
How much television were American adults watching in 2014 (TVHOURS)? Produce a histogram to help answer the question.
Modern Furnitures was established in 2000. Its products include household and office furniture. It has grown organically with new designs of furniture as well as through acquisition of other...
$ 143 is placed in an account that earns a nominal 8 percent interest, compounded quarterly. Calculate its worth in 8 years. Use 2 decimal places for your final answer.
labour cost. Last year, the company sold 30,000 of these balls, with the following results: Sales (30,000 balls) $750,000 Variable expenses Contribution margin 450,000 300,000 Fixed expenses...

If Vis a vector space over a division ring and fa V*, let W = I a

Question:

Step by Step Answer:

ANSWER Since f is a nonzero linear function on V ...View the full answer

Algebra Graduate Texts In Mathematics 73

Students also viewed these Mathematics questions