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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.
The equation and variables below is similar to the above equation, However, the A is on the sum side. Can someone show me the steps in this process.
why is zero excluded from the domain of a logarithmic function?is every rational function a polynomial function?
justin is using 120 inches of wire to build two structures 1 one rectangle that is five times as long as it is wide and
Let n be an integer.
Simplifying the equation.
An object is close to a light source - say at a distance of x meters. Another object B is at a distance of 2.3 times x meters from the same light source or in equation from distance to B from the light source = 2.3 (x meters).
Make the fractions of the LCM of the denominators.
Solve quadratic equations.
A restaurant has an annual demand for 900 bottles of a California wine. It costs $1 to store one bottle for one year, and it costs $5 to place a reorder. Find the number of orders that should be placed annually.
What would your answers be if we considered the open balls B∈(ζ) for different values of ∈? What if we also thought about the balls for the the d2 metric?
The graph of an exponential function
Imagine that every single person in your contact list has the same number of people in their contact list as you. Write this total number of all the contacts in all the phones (ignore the fact that some may repeat) as an exponential. Next, evaluat..
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