Solution-Prove that if m is a maximal ideal of s

Prove that if m is a maximal ideal of s

Reference no: EM131027763

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: EM131027763

Questions Cloud

About equity theory : Let's talk about Equity Theory. The gist of this theory is that by nature we compare ourselves to our neighbor. So we measure what happens to them and might adjust our behavior accordingly. So how do we determine equity? What are some examples of thi..

Market research and continuous improvement in development : Pretend that you are starting up your own computer sales business. Based on what you have learned about market research so far, how will you approach market research and continuous improvement in the development of your new business?

Explain how this strategy influences total cost of ownership : Evaluate one of the geographic locations that this supply chain operates in (see Part A network diagram). Explain how this location fits this supply chain network design. Identify the pros and cons for that phase of the supply chain as to how that..

Show that p is a subgroup of the direct product of the group : Show that if all A_i are commutative rings with 1 and all phi_ji are ring homomorphisms that send 1 to 1, then A may likewise be given the structure of a commutative ring with 1 such that all phi_i are ring homomorphisms.

Prove that if m is a maximal 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.

Problem related to sec complaint : Read the release and the related SEC Complaint. Summarize the release and complaint in 2-3 pages (12-point, double spaced).

What is difference between ideal culture and real culture : What is the difference between ideal culture and real culture? What do people not follow the ideal culture? Why does a culture still support the ideal culture while behaving according to the real culture

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)

User Account

All Pages

Prove that if m is a maximal ideal of s

Reference no: EM131027763

Reference no: EM131027763

Questions Cloud

Reviews

Write a Review

Algebra Questions & Answers

Determining elasticity and revenue

What is the difference between domain and range

Compute the value of y in the mod 9 system

What constitutes a rational expression

Determining radicals and rational exponents

Find the cost function and the average cost functions

Provide an example of using distributive property for

Find the opposite of the polynomial

Mark each statement true or false

Language arts literacy skills

Force diagrams-vectors and equations of motion

Equations that prove the associative property

Assured A++ Grade

Academics

Major Subjects

Majors

Get In Touch

TERMS & POLICIES

HELP & SUPPORT