Let G,H,K be divisible abelian groups. (a) If G G HH, then G H
Question:
Let G,H,K be divisible abelian groups.
(a) If G ⊕ G ≅ H⊕H, then G ≅ H [see Exercise 11].
(b) If G⊕H ≅ G⊕K, then H ≅ K [see Exercises 11.].
Data from exercise 11
Every divisible abelian group is a direct sum of copies of the rationals Q and copies of Z(p∞) for various primes p.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 63% (11 reviews)
a If G G H H then G H Since G and H are divisible abelian groups we can write them as direct sums of ...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
-
Every divisible abelian group is a direct sum of copies of the rationals Q and copies of Z(p) for various primes p.
-
(a) Let G be a finite abelian p-group (Exercise 7). Show that for each n 0, p n+1 G G[p] is a subgroup of p n G G[p].(b) Show that (p n G G[p])/(p n+1 G G[p]) is a direct sum of copies of Z p ;...
-
Every torsion-free divisible abelian group D is a direct sum of copies of the rationals Q. if O n e Z and D, then there exists a unique b D such that nb = a. Denote h by (1/n)a. For m, n Z (n ...
-
How does ESMA support national regulators in enforcing the application of IFRS?
-
If the U.S. government is indebted $200, and if $100 is in the form of an externally held public debt, while another $100 is an internally held public debt, the impacts of these two different debts...
-
Assume that when a purchase of supplies of $2,650 for cash was recorded, both the debit and the credit were journalized and posted as $2,560. (a) Would this error cause the trial balance to be out of...
-
Use the USDA Quick Stats service (http://quickstats.nass.usda.gov//) to compare the 2009 oat yields between New York and California. What additional land would California require to meet the same...
-
Steve and Linda Hom live in Bartlesville, Oklahoma. Two years ago, they visited Thailand. Linda, a professional chef, was impressed with the cooking methods and the spices used in the Thai food....
-
What is the relationship between diversity, inclusion, and mental health in the workplace, and how can organizations create supportive environments that address the unique mental health needs of a...
-
A painting operation is scheduled in blocks, where each block involves painting products with a particular color. Cleaning time is required in between each pair of blocks so that the equipment can be...
-
Let F be a field, X an infinite set, and V the free left F-module (vector space) on the set X. Let F x be the set of all functions. : X F. (a) F x is a (right) vector space over F (with ( + g)(x) =...
-
Let F be a free module of infinite rank a over a ring R that has the invariant dimension property. For each cardinal such that O , F has infinitely many proper free submodules of rank .
-
What is the general procedure for developing a level production plan in a make-to-order environment?
-
By applying modern technology to agriculture, the United States has become the most productive food-producing nation in the world. The secret to solving the world food security problem lies in...
-
What are the income-distribution consequences of fashion? Can the need to be seen driving a new car by the rich be a boon to those with lower incomes who will ultimately purchase a better,...
-
In your hometown what system is used to price the publicly supplied water? Why was that pricing system chosen? Would you recommend an alternative?
-
Many areas have attempted to increase the amount of recycled waste lubricating oil by requiring service stations to serve as collection centers or by instituting deposit-refund systems. On what...
-
One current practice is to calculate the years remaining for a depletable resource by taking the prevailing estimates of current reserves and dividing it by current annual consumption. How useful is...
-
Give two possible sets of four quantum numbers for the electron in an H atom.
-
Question 2 For an n x n matrix A = form) via (aij)
-
What proportion of people have borderline cholesterol? Suppose a person is regarded as having high cholesterol if Z > 2.0 and borderline cholesterol if 1.5 < Z < 2.0.
-
What percentage of boys in this age range have carbohydrate intake above 140 g/1000 cal? Nutrition Suppose that total carbohydrate intake in 12- to 14-year old boys is normally distributed, with mean...
-
What percentage of boys in this age range have carbohydrate intake below 90 g/1000 cal? Nutrition Suppose that total carbohydrate intake in 12- to 14-year old boys is normally distributed, with mean...
-
You have just been assigned as the manager of an engagement with an audit client. before you start working on the engagement, what steps
-
GHI Corporation is planning to grow 15% per year while maintaining a debt-equity ratio of 1.3 and dividend payout ratio of 35%. The ratio of total asset to sales is constant at .80. What profit...
-
Discuss the division of responsibilities of CRA for payroll functions.
Study smarter with the SolutionInn App