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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.
Demostrate the complete proof of the Cauchy-Schwarz inequality and the triangle inequality.
Find the x- and y-intercepts of each graph(write your answers as points). Write the equation of the line through (3, -2) and (-1, 5) (slope-intercept form). Write the equation of the line parallel to 3x - 2y = 4 through (-2, 5).
explain what it means for a rational equation to have more than one solution. provide an example of a rational
Trains A and B are traveling in the same direction on parallel tracks. Train A traveling at 80 miles per hour and train B is traveling at 84 miles per hour. Train A passes a station at 9:25 A.M. If train B passes the same station at 9:55 A.M., at ..
I will be demonstrating how to evaluate and create a two- variable inequality. This means there are two different variables included into an inequality.
Let a subset A of the real numbers R be co-countable provided that R - A is countable. Show that the set of all countable and co-countable subsets of R is a sigma- algebra.
Solve the system using the elimination method
Express the solution of the compound inequality in interval notation. Express the solution of the compound inequality in interval notation y>=5 or y>1
the approximate population of san diego california between 1960 and 1990 can be modeled by the function
Evaluate the function at the given value of the independent variable and simplify. Evaluate the function at the given value of the independent variable and simplify.
Stop and Wait ARQ, SENDER sends four frames (F1, F2, F3, and F4). F1, F2 and F4 are received error free, but F3 is lost in the network during its initial transmission. Continue the diagram until all frames are received are error free and properly ..
Simplify the algebraic expression 3x 2 - 2y + 7x 2 - 5y + 3 and evaluate it for x = 2, y = 14. Identify the variables, constants, and coefficients in the simplified expression.
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