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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.
Business and finance. When x number of units are sold, the price of each unit (in dollars) is given by P=-x/2 + 75. Find the unit price when the following quantities are sold: 2, 7, 9, 11.
Apply the order of operations to solve.
the population of a city was 94 thousand in 1992. the exponential growth rate was 1.6 per year. find the exponential
Current in a circuit: The current in a simple electrical circuit varies inversely as the resistance. If the current is 50 amps when the resistance is 10 ohms, find the current if the resistance is 5 ohms.
Explain the difference between the two. Give two examples of relations and two examples of functions. What does it mean to evaluate a function?
Find the solution for y
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Describe the various decisions for Esil University that would be affected by the forecast for undergraduate applications.
In 1999, the expectancy of males in a certain country was 65.5. In 1995, it was 68.0 years. Let E represent the life expectancy in year T represent the numbers of years since 1991.
What are the other 2 eigenvalues of A and what is the characteristic polynomial of A, At, and A-1?
How would you use this procedure to determine if a given polynomial is prime, that is, determine that it cannot be factored into a product of two linear polynomials (note pps 321 and 327 of the text, Prime Polynomials)?
Find the solution of the problem
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