User Account

All Pages

Prove that if p is a prime ideal of s

Assignment Help Algebra
Reference no: EM131027756

Let phi:R->S be a homomorphism of commutative rings

a) Prove that if P is a prime ideal of S then either phi^-1(P)=R or phi^-1(P) is a prime ideal of R. Apply this to the special case when R is a subring of S and phi is the inclusion homomorphism to deduce that if P is a prime ideal of S then PR is either R or prime ideal in R

b) Prove that if M is a maximal ideal of S and phi is surjective then phi^-1(M) is maximal ideal of R. Give an example to show that this need not be the case if phi is not surjective.

Reference no: EM131027756

Questions Cloud

Relationship between projects scope and its budget : Describe the relationship between a project’s scope and its budget and your experience with both. What may occur with a project if it is over budget with a significant scope remaining? Please provide references.
Describe the employee search process you would use : Describe testing you would employ. Describe interviewing approaches you would use. Discuss issues you might encounter.6. develop a forecast of anticipated demand for this welding company and availability in the labor market (federal and state data)
Date the property dividend : ABC is selling for $10 per share on the date the property dividend is declared. (e) Myers declares a 2-for-1 stock split and issues new shares.
Southwest airlines case study-is luv soaring or sour : Analyze and summarize the key attributes of Southwest’s culture and its intellectual assets. Discuss how the Company can use these attributes to adapt, change, and continue to grow as the environment in which the Company does business changes. You ma..
Prove that if p is a prime ideal of s : Prove that if M is a maximal ideal of S and phi is surjective then phi^-1(M) is maximal ideal of R. Give an example to show that this need not be the case if phi is not surjective.
Unrelated product diversification : Unrelated product diversification (conglomeration) is widely discredited in developed economies; however, in some cases it appears to add value in emerging economies. Is this interest in conglomeration likely to hold or decrease in emerging economies..
How reliable do you find rating agencies ratings : How does credit rating affect an investor's required rate of return? What actions could a firm take to receive a more favourable rating and how reliable do you find rating agencies' ratings in general? Also discuss credit ratings from the point of..
How does the family help with the functions of socialization : How does the family help with the functions of Socialization? Use of the socialization processes to help explain how the family fulfills the functions of the family
What is thought to be the source of the sulfur dioxide : What is thought to be the source of the sulfur dioxide that was released into the atmosphere following the impact at Chicxulub? What characteristics of hurricanes are NOT also associated with individual thunderstorms?

Reviews

Write a Review

Algebra Questions & Answers

  Find the value of x by the properties of logarithms

Find the value of x by the properties of logarithms.

  Linear equation that gives the annual benefit

There is a linear equation that gives the annual benefit b in terms of age a for these three years. Find the equation.

  Solve the system of equations using matrices

Solve the system of equations using matrices and the Gaussian Elimination Method with back substitution method 2x+y-2z=-1

  Find the smallest integer

The sum of four consecutive even integers is 2 more than five times the first integer. Find the smallest integer

  Prove that there are no matrices

Show that the trace is a linear map of the space of n n matrices into K.

  Solve one side of the problem correctly

Point for solve one side of the problem correctly and points for solve both sides of the problem correctly

  Graphical and numerical methods for equations

Explain the difference between solving a system of equations by the algebraic method and the graphical method to a sixth grader?

  Find the equation of lest square line

Draw a scatter plot and find the equation of the lest square line for the given data. From the least square equation, find the percentage for year 1999.

  Develop a linear regression model for these data

Describe the various decisions for Esil University that would be affected by the forecast for undergraduate applications.

  Find the lcm of the denominators

Find the LCM of the denominators

  How are these examples different from others

Since each pupa of morpho granadensis costs $4.15 and p pupae were received, 4.15p is the cost for the morpho granadensis species. Similarly, 1.50q is the cost of the battus polydamus species. From the third row of the table and the information in..

  Find the cost of one washer and one dryer

Another appliance store buys 4 washers and 5 dryers from the same wholesale supplier at a total cost of $1561. Find the cost of one washer and one dryer.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

Submit Assignment

Academics

Major Subjects

Majors

Get In Touch

whatsapp: +1-415-670-9521

Phone: +1-415-670-9521

Email: [email protected]

TERMS & POLICIES

HELP & SUPPORT

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd