If F is a free module over a ring with identity such that F has a basis
Question:
If F is a free module over a ring with identity such that F has a basis of finite cardinality n ≥ 1 and another basis of cardinality n + 1, then F has a basis of cardinality m for every m ≥ n (m ϵ N*).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 85% (7 reviews)
Let R be a ring with identity and F be a free module over R with a basis of finite cardinality n 1 and another basis of cardinality n 1 We want to sho...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
-
If one attempted to dualize the notion of free module over a ring R (and called the object so defined "co-free") the definition would read: An R-module F is co-free on a set X if there exists a...
-
Let R be a ring with identity. Show that R is not a free module on any set in the category of all R-modules (as defined in Exercise 2). Data from in exercise 2 Let R be any ring (possibly without...
-
Let R be any ring (possibly without identity) and Fa free R-module on the set X, with L : X F, as in Exercise 2. Show that L (X) is a set of generators of the R-module F. is commutative. Conclude...
-
What are the institutional features that appear to have delayed the implementation of IFRS in India?
-
Admitting all exceptions to the rule, the rule is that free trade benefits all nations. Make the case.
-
This essay is on the film KING CORN. Your essay must answer the following questions in essay form (NOT short/long answer) , using APA formatting and citations. 3-5 pages not counting cover and...
-
A realtor who flips houses (purchases and remodels them with the goal of reselling them for profit) has collected data on a variety of house characteristics and selling prices for a sample of 1,198...
-
One of the major problems that Bohn faced was that only about 40 percent of the jobs listed for scheduled maintenance shutdowns were ever performed. During an informal conversation with Ken Viet,...
-
What are some of the factors that make it difficult for unions to coordinate their efforts across national borders? What is a great personal branding statement for a cyber-security human resources...
-
Coverall Inc. produces and sells a unique type of case for a standard size tablet computer that is guaranteed waterproof but still allows for regular functionality of the tablet. The company has just...
-
Proof that Let K be a ring with identity and Fa free K-module with an infinite denumerable basis {e 1 ,e 2 , ... }. Then R = Hom K (F,F) is a ring by Exercise 1. 7(b). If n is any positive integer,...
-
Assume R has an identity. Let be the category of all unitary R-R bimodules and bimodule homomorphisms (that is, group homomorphisms : A B such that (ras) = r(a)s for all r,s R). Let X = { 1 R }...
-
Classify the following sets as finite or infinite. a. The set of people who are living or who have ever lived b. The set of grains of sand on all the beaches on Earth
-
(2) Draw a histogram with the bin size of 10 (bins: 70 < Ax 80, 80 < Ax 90, ... ... ) and fit the histogram with a normal distribution function (or normal Gaussian function) as follows and find the...
-
Kit Inc., a manufacturer of kitchen cabinets, sells cabinets for $16,000 per set. Kit is now considering developing a new set of cabinets for a condominium project. The estimated costs are $12,000...
-
Vanessa earned scores of 72, 96, 68, and 81 on the four exams in the class. What was her mean exam score? Round your answer to the nearest whole number
-
Mahogany's new finance director has read about review engagements and is interested in the possibility of DWM & Co undertaking these in the future. However, she is unsure how these engagements differ...
-
[142] (i) Find the general solution of the homogeneous equation Ar = 0. Assume that A (ii) Find solutions of Az = 2 (iii) Find the general solution of the equation in part (ii). 3 (iv) Find solutions...
-
How much will it cost in Canadian dollars to purchase 2000 pesos in Mexican currency at a bank that charges a 3.5% commission on the transaction? Use an exchange rate of C$1.00 = Mexican peso 11.87.
-
1. Firms may hold financial assets to earn returns. How the firm would classify financial assets? What treatment will such financial assets get in the financial statements in accordance with US GAAP...
-
Researchers often use z tests to compare their samples to known population norms. The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black-and-white drawings. The test,...
-
In your own words, define the word effectfirst as you would use it in everyday conversation and then as a statistician would use it.
-
In an exercise in Chapter 7, we asked you to conduct a z test to ascertain whether the Graded Naming Test (GNT) scores for Canadian participants differed from the GNT norms based on adults in...
-
Read Lumber Sales Inc. v. Julious Brown and consider the Critical Thinking Questions, The goal of this assignment is start to learn lessons from cases and translate them into business actions. This...
-
Patterson Development sometimes sells property on an installment basis. In those cases, Patterson reports income in its income statement in the year of the sale but reports installment income by the...
-
Design a program to combat a type of violence of your choice that will include elements of both primary and secondary prevention. What factors of your program are directed toward primary prevention,...
Study smarter with the SolutionInn App