If F is a field, then (x) is a maximal ideal in F[x], but it is not

Question:

If F is a field, then (x) is a maximal ideal in F[x], but it is not the only maximal ideal (compare Corollary 5.10).

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 03:51 AM

See More Questions

Proof that: (a) If F is a field then every nonzero element of F[[x]] is of the form x k u with u F[[x]] a unit. (b) F[[x]] is a principal ideal domain whose only ideals are 0, Fl[x]] = (1 F ) = (x O...
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
Give a one- or two-sentence synopsis of "if' part of Theorem 27.9. Data from Theorem 27.9 Let R be a commutative ring with unity. Then M is a maximal ideal of R if and only if R/M is a field. Proof...
Is an isothermal process necessarily internally reversible? Explain your answer with an example.
What are some of the limitations in using GDP as a measuring rod of our economic well-being?
Question 5 (25 marks) Siyabakulisa (Pty) Ltd is a small manufacturing company. The company's accounting functions are carried out by the accounting staff consisting of the accountant, Zandile Zulu,...
What is the composition of dry air?
Eclipse Motorcycle Shop sells motorcycles, ATVs, and other related supplies and accessories. During the taking of its physical inventory on December 31, 2012, Eclipse Motorcycle Shop incorrectly...
Pepsico Inc. announced yesterday that it would spin off its KFC, Pizza Hut and Taco Bell restaurant businesses as a publicly traded company, one that would be second only to McDonald's in the fast...
The Apex Television Company has to decide on the number of 65 and 55 sets to be produced at one of its factories. Market research indicates that at most 280 of the 65 sets and 70 of the 55 sets can...
Let R be a commutative ring with identity, I an ideal of R and : R R/ I the canonical projection. (a) If S is a multiplicative subset of R, then S = (S) is a multiplicative subset of R/ I. (b) The...
(a) The polynomial x + I is a unit in the power series ring Z[[x]], but is not a unit in Z[x]. (b) x 2 + 3x + 2 is irreducible in Z[[x]], but not in Z[x].
The optomotor responses of tree frogs were studied in the Journal of Experimental Zoology (Sept. 1993). Microspectrophotometry was used to measure the threshold quantal flux (the light intensity at...
Anusha and Bill went to the Royal Easter show where each of them bought identical toys. Both lost their toys on their way back home. Their parents decided to reimburse them. They do not know the...
1. Elsinore assumes it can grow its dividend by 5% a year forever. If the last dividend paid was $2 and the required rate of return is 10%, what is the current share price (approximately)? 2. a) $40...
A moving component is subjected to vibrations along its length, emanating from two machines situated at opposite ends. The displacement caused by the vibrations can be modelled by the following...
Earnings before interest and tax (EBIT) Equity share capital (1000 shares of *10 each) Preference and debt capital Change in EBIT Corporate tax 20,000 10,000 Nil +/- 25% 50% You are required to: a)...
Please show your work and explain how you got your answer along the way. Do not simply show an answer or show a picture of an excel spreadsheet please. The following table gives data on daily dollar...
Mountain Sports is advertising 30% Off All Skiing Equipment in its Spring Clearance Sale. On ski boots marked down to $348.60, what is the regular price?
What is a make-or-buy decision?
Implement the test procedure in Problem 7.52, and report a p-value (two-sided)? Ophthalmology Researchers have reported that the incidence rate of cataracts may be elevated among people with...
Test the hypothesis that the 5-year incidence rate of cataracts is different in the excessive-sunlight-exposure group compared with the general population, and report a p-value (two-sided). The...
Construct a 95% CI for the 5-year true rate of cataracts among the excessive-sunlight-exposure group? The researchers decide to extend the study to a 5-year period and find that 20 of the 200 people...
A 0.45 kg baseball is pitched at -47m/s. After being hit by the batter it has a velocity of 50 m/s. The batter generates 30,000N of force in the swing. Why is one of the velocities negative? What is...
A 1500kg Ferrari accelerates out of a turn from 20m/s to 40m/s in 3s. What is the force required by the engine to perform this acceleration? What is the impulse felt by the driver? Calculate the...
The International Space Station (ISS) is orbiting Earth at an altitude of approximately 400 km. The mass of the ISS is approximately 4.0 105 kg. The radius and mass of Earth are approximately 6.4 106...

If F is a field, then (x) is a maximal ideal in F[x], but it is not

Question:

Step by Step Answer:

Recall that an ideal I of a ring R is maximal if I is proper ie I R and the only ideals containing I ...View the full answer

Algebra Graduate Texts In Mathematics 73

Students also viewed these Mathematics questions