(a) Let G be the additive group of all polynomials in x with integer coefficients. Show that...
Question:
(a) Let G be the additive group of all polynomials in x with integer coefficients. Show that G is isomorphic to the group Q* of all positive rationaJs (under multiplication).
(b) The group Q* is free abelian with basis {p|p is prime in Z}.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 60% (5 reviews)
a To show that G is isomorphic to Q we need to construct a bijective group homomorphism between them Consider the map G Q defined by fx 2degf p1e1 pnen where degf is the degree of the polynomial f p1 ...View the full answer
Answered By
Mary Boke
I have teached the student upto class 12th as well as my fellow mates.I have a good command in engineering,maths and science.I scored 90+ marks in 10th and 12th in maths.
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 G = S4, the symmetric group on four symbols, and let H be the subset of G where (a) Construct a table to show that H is an abelian subgroup of G. (b) How many left cosets of H are there in G? (c)...
-
Referring to Example 24.3, show that YX - XY = 1. Data from in 24.3 Example Let F be a field of characteristic zero, and let (F[x], +) be the additive group of the ring F[x] of polynomials with...
-
Let G be the additive group of real numbers. Let the action of G on the real plane R 2 be given by rotating the plane counterclockwise about the origin through radians. Let P be a point other than...
-
For publicly traded companies, the Sarbanes-Oxley Act prescribes fines and prison time for knowingly falsifying financial information. Further, investors of the company may be able to successfully...
-
Why do unions strike? Do strikes always benefit workers?
-
Cultural influences often create externalities, for good and ill. A happy movie might make people smile more, which improves the lives of people who don't see the movie. A new fashion trend for...
-
What are the final two steps a researcher should do after presenting the research findings to the decision makers?
-
Brian and Gary are college friends planning a skiing trip to Killington before the New Year. They estimated the following costs for the trip: Requirements 1. Brian suggests that the costs be shared...
-
1. Consider the following modification to the MergeSort algorithm: divide the input array into fourths (rather than halves), recursively sort each sort each forth, and finally combine the results...
-
What is each shareholder's realized gain or loss? b. What is each shareholder's recognized gain or loss? c. What is each shareholder's basis in their stock? When does their holding period begin? d....
-
Show that every automorphism of S 4 is an inner automorphism, and hence S 4 Aut S 4 .
-
(a) Show that the analogue of Theorem 7.11 is false for nilpotent groups [Consider S 3 ]. (b) If H < C( G) and G/H is nilpotent, then G is nilpotent. Theorem 7.11 (i) Every subgroup and every...
-
Here are some questions for practicing unit conversions: (a) How long is a nanoyear in seconds? (b) Micrometers are often called microns. How long is a megamicron? (c) How many bytes are there in a...
-
(a) Define Mach number and Mach angle. (b) Give an expression that represents sonic speed in an arbitrary fluid. (c) Give the relation used to compute sonic speed in a perfect gas.
-
FASB, GAAP, SEC, CPA, AICPA, IRS, IASB, IFRS are all acronyms used in accounting. For the preceding list of acronyms, state what the acronym stands for and then give a definition of each acronym.
-
Allendorf Company used $90,000 in cash to purchase land on the west side of Hatu Lake. a. List the accounts impacted by the transaction. b. For each account, indicate whether the transaction...
-
Allendorf Company received $180,000 in cash as an additional investment by the stockholders (owners) of the company. a. List the accounts impacted by the transaction. b. For each account, indicate...
-
Assume the same facts as in Problem 29, except that Sally has AGI of \($75,000.\) What is her qualified student loan interest deduction in 2019? Problem 29, In 2019, Sally Morris, a single taxpayer,...
-
In the previous problem, we studied the effects of a cost-saving invention. For this problem, we suppose that there was no such invention, but that a tax is introduced. Suppose that on January 1,...
-
Suppose the market is semistrong form efficient. Can you expect to earn excess returns if you make trades based on? a. Your brokers information about record earnings for a stock? b. Rumors about a...
-
Implement the test in Problem 8.99, and report a p-value? Endocrinology A study was performed to determine the effect of introducing a low-fat diet on hormone levels of 73 postmenopausal women not...
-
Provide a 95% CI for the change in mean log10 (plasma estradiol)? Endocrinology A study was performed to determine the effect of introducing a low-fat diet on hormone levels of 73 postmenopausal...
-
Construct a two-sided 90% CI for the mean change score for retired women. What does it mean? Health Promotion A study looked at the influence of retirement on the level of physical activity among...
-
What role do institutions and governance systems play in fostering an environment conducive to empowerment, and how can these structures be reimagined to better serve marginalized populations ?
-
On January 1, 2009, Bruno owed $8,384 to his friend Alexandra, who was kind enough not to charge Bruno any interest. Each month during 2009, Bruno paid Alexandra some of the money he owed. If Bruno...
-
Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of...
Study smarter with the SolutionInn App