(a) If A and Bare R-modules, then the set Hom R (A,B) of all R-module homomorphisms A...
Question:
(a) If A and Bare R-modules, then the set HomR(A,B) of all R-module homomorphisms A → B is an abelian group with ∫ + g given on a ϵ A by(∫+ g)(a) = f(a) + g(a) ϵ B. The identity element is the zero map.
(b) HomR(A,A) is a ring with identity, where multiplication is composition of functions. HomR(A,A) is called the endomorphism ring of A.
(c) A is a left HomR(A,A)-module with ∫a defined to be
Transcribed Image Text:
f(a) (a e A,fe HomR(A,A)).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 83% (6 reviews)
a The set HomRAB is an abelian group under pointwise addition since the sum of two Rmodule homomorph...View the full answer
Answered By
User l_917591
As a Business Management graduate from Moi University, I had the opportunity to work as a tutor for undergraduate students in the same field. This experience allowed me to apply the theoretical knowledge I had gained in a practical setting, while also honing my teaching and communication skills.
As a tutor, I was responsible for conducting tutorial sessions, grading assignments and exams, and providing feedback and support to my students. I also assisted with the preparation of course materials and collaborated with other tutors and professors to ensure consistency in teaching and assessment.
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...
-
Show that the multiplication defined on the set F of functions in Example 18.4 satisfies axioms R2 and R3 for a ring. Data from 18.4 Example Let F be the set of all functions f: R R We know that (F,...
-
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...
-
Do you think that differences in reward practices across countries reflect differences in national cultures or other influences?
-
Suppose the Federal Reserve raised the reserve requirement to 50 percent. Show how that would affect the value of money creation through the first 5 stages of deposit and loan in practice problem 1....
-
During its first year of operations, Master Plumbing Supply Co. had net sales of $3,500,000, wrote off $50,000 of accounts as uncollectible using the direct write-off method, and reported net income...
-
Write an audit programme to carry out an environmental audit in a university. The organisation has never in its history been through an environmental audit.
-
Portland Products is considering the purchase of one of three mutually exclusive projects for increasing production efficiency. The firm plans to use a 14% cost of capital to evaluate these...
-
Object A has a mass of 4.8 kg and is moving at 4.5 m/s when it collides head-on with a stationary object B of mass 6.0 kg. Object A rebounds directly backward with a velocity of 0.50 m/s while object...
-
Suppose your company introduces a referral incentive for existing customers. Namely, cus- tomers can get a $500 discount on their customer service subscription for each customer lead that they refer...
-
(a) For each prime p, Z(p) is a divisible group. (b) No nonzero finite abelian group is divisible. (c) No nonzero free abelian group is divisible. (d) Q is a divisible abelian group.
-
If R has an identity, then every unitary cyclic R-module is isomorphic to an R-module of the form R/J, where J is a left ideal of R.
-
Design a linear-phase lapped biorthogonal transform with \(M=6\) sub-bands aiming at minimizing the stopband ripple of the sub-filters.
-
A creditor most likely would consider a decrease in which of the following ratios to be positive news? A. Interest coverage (times interest earned). B. Debt-to-total assets. C. Return on assets.
-
When developing forecasts, analysts should most likely : A. develop possibilities relying exclusively on the results of financial analysis. B. use the results of financial analysis, analysis of other...
-
Which of the following ratios would be most useful in determining a companys ability to cover its lease and interest payments? A. ROA. B. Total asset turnover. C. Fixed charge coverage.
-
Golden Cumulus Corp., a commodities trading company, reported interest expense of $19 million and taxes of $6 million. Interest payable increased by $3 million, and taxes payable decreased by $4...
-
In order to assess a companys ability to fulfill its long-term obligations, an analyst would most likely examine: A. activity ratios. B. liquidity ratios. C. solvency ratios.
-
What mass of H2O can be heated from 22(C to 80(C in the combustion of 1 mol of C2H6? You will need the balanced thermo chemical equation for the combustion of C2H6.
-
A superior criticized a sales manager for selling high-revenue, low-profit items instead of lower-revenue but higher-profit items. The sales manager responded, My income is based on commissions that...
-
Based on the results in Problem 5.56, should the program be implemented? Why or why not? The program will be implemented if at least 50% of the GDM women in the program are no more than 2 lbs. above...
-
A study was conducted relating particulate air pollution and daily mortality in Steubenville, Ohio [4]. On average over the past 10 years there have been 3 deaths per day in Steubenville. Suppose...
-
What proportion of 50-year-old women is hypertensive, if hypertension is defined as SBP 140 mm Hg? Cardiovascular Disease Obesity is an important determinant of cardiovascular disease because it...
-
What role does customer advocacy play in word-of-mouth marketing and brand advocacy?
-
Direct materials cost per unit Direct labor cost per unit Sales price per unit Expected production per month Home $ 40 21 364 Work $ 64 35 578 660 units 350 units Harbour has monthly overhead of...
-
Harbour Company makes two models of electronic tablets, the Home and the Work. Basic production information follows: Direct materials cost per unit Direct labor cost per unit Sales price per unit...
Study smarter with the SolutionInn App