Let R be a finite commutative ring with unity. Show that every prime ideal in R is

Question:

Let R be a finite commutative ring with unity. Show that every prime ideal in R is a maximal ideal.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

See More Books

Question Posted: Jan 05, 2023 05:26 AM

See More Questions

Let R be a commutative ring with unity u. a) For any (fixed) a R, prove that aR = {ar| r R] is an ideal of R. b) If the only ideals of R are {z} and R, prove that R is a field.
Let R be a commutative ring with unity u, and let I be an ideal of R. (a) If u 1, prove that I = R. (b) If I contains a unit of R, prove that I = R.
Let R be a commutative ring with unity of prime characteristic p. Show that the map p : R R given by p (a) = a P is a homomorphism (the Frobenius homomorphism).
Selenic acid, H2SeO4, is a crystalline substance and a strong acid. Write the electron-dot formula of selenic acid.
(a) We find that .40 of a sample of 500 people score above 60. How many people scored above 60? (b) In statistical terms, what are we asking about a score when we ask how many people obtained the...
Africa offers a fast growing and exciting mobile phone market, with more than 50% growth per year since 2002. More than 28% of African consumers own mobile phones; a larger market than North America....
C8.4. Inaccounting fur theconversion ofconvertible bondstocommon stock,mostfirms recordthe issueof sharesat theamount of thebookvalueof the bonds. The issue of the sharescouldbe recorded at their...
The assets of Fonzarelli Corporation are presented on the next page (000s omitted).InstructionsIndicate the deficiencies, if any, in the foregoing presentation of Fonzarelli Corporation??sassets....
FINANCIAL PROJECTIONS EXERCISE (CASE STUDY) (Ms. LeBlanc, Inc.) This case exercise is designed to give you some practical, hands-on experience in preparing pro forma financial projections. Please...
The cantilevered beam AB is additionally supported using two tie rods. Determine the force in each of these rods. Neglect axial compression and shear in the beam. For the beam, I b = 200 (10 6 ) mm 4...
Show that a factor ring of a field is either the trivial (zero) ring of one element or is isomorphic to the field.
Find a Grobner basis for the given ideal in R[x, y]. Consider the order of power products to be lex with y < x. If you can, describe the corresponding algebraic variety in R[x, y]. (x 2 y - x - 2,xy...
A man of height 1.8 m walks away from a 5-m lamppost at a speed of 1.2 m/s (Figure 10). Find the rate at which his shadow is increasing in length. 5 X
Below are incomplete financial statements for Hurricane, Incorporated Required: Calculate the missing amounts. Complete this question by entering your answers in the tabs below. Income Statement Stmt...
TBTF Incorporated purchased equipment on May 1, 2021. The company depreciates its equipment using the double-declining balance method. Other information pertaining to the equipment purchased by TBTF...
Coco Ltd. manufactures milk and dark chocolate blocks. Below is the information relating to each type of chocolate. Milk Chocolate Selling price per unit $6 Variable cost per unit $3 Sales mix 4 Dark...
Data related to 2018 operations for Constaga Products, a manufacturer of sewing machines: Sales volume 5,000 units Sales price $300.00 per unit Variable production costs Direct materials 75.00 per...
6. (20 points) Sections 3.1-3.5, 3.7 Differentiate the following functions, state the regions where the functions are analytic. a. cos(e*) b. 1 ez +1 c. Log (z+1) (Hint: To find where it is analytic,...
Determine the mean, median, mode, and midrange of the set of data. Where appropriate, round your answer to the nearest tenth. 4, 6, 7, 7, 7, 9, 9
Perform the indicated operations. In designing a cam for a fire engine pump, the expression is used. Simplify this expression. (3) (3 4 32
According to Remodeling magazine, the average cost to convert an existing room into a home office with custom cabinetry and rewiring for electronic equipment is $5976. Assuming a population standard...
Under what circumstances should the t-statistic be used in carrying out a hypothesis test for the population mean?
The average length of a flight by regional airlines in the United States has been reported as 299 miles. If a simple random sample of 30 flights by regional airlines were to have x =314.6 miles and s...
Los datos de la columna C tienen caracteres no imprimibles antes y despus de los datos contenidos en cada celda. En la celda G2, ingrese una frmula para eliminar cualquier carcter no imprimible de la...
Explain impacts of changing FIFO method to weighted average method in inventory cost valuations? Explain impacts of changing Weighted average method to FIFO method in inventory cost valuations?...
A perpetuity makes payments starting five years from today. The first payment is 1000 and each payment thereafter increases by k (in %) (which is less than the effective annual interest rate) per...

Let R be a finite commutative ring with unity. Show that every prime ideal in R is

Question:

Step by Step Answer:

Every finite integral domain is a field ...View the full answer

A First Course In Abstract Algebra

Students also viewed these Mathematics questions