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Topic: Abstract Algebra
Question: Let Θ be a congruence on a distributive lattice with 0. Define IΘ (subscript Θ) = O/Θ. Prove that IΘ (subscript Θ) is an ideal of D.
Show that for any ideal I of a distributive lattice D with O, that IΘI (subscript ΘI ) = I. Give an example of a congruence Θ on a distributive lattice D with 0 where ΘIΘ (subscript IΘ) ≠ Θ.
Show that if B is a Boolean algebra, then for any congruence Θ of B that ΘIΘ = Θ (subscript IΘ).
Give an example of a complete distributive lattice that is not isomorphic to D(P), the collection of downsets of P, for any poset P and prove.
For a finite poset P prove that P is an order-isomorphism to the poset β(D*(P)) where D*(X) is the collection of downsets of X and β(D)={P| P is a prime ideal, I≠0, I≠D}.
Solving equation by using arithmetic operations.
Band members at Colchester Middle School are expected to average at least 20 min of practice time per day. One week Monroe practiced 15 min, 28 min, 30 min, 0 min, 15 min, and 25 min. How long must he practice on the seventh day if he is to meet e..
Graph the basic function using a solid line and the transformed function using a dotted line.
Make a graph for quadratic function.
The length of a rectangular parking lot is 40 ft more than the width. If the parking lot is iv feet wide, express its area as a function of the width.
If you made all A's all the way through, how much would the last grading period be worth? Create an equation to represent any grading period along the way
Three numbers, whose sum is 12, are in AP. If 1,2 and 6 are added to them, the resulting g numbers are in GP. Find the numbers
Name the variables: x is the number of 2-point baskets and y is the number of 3-pointers. Set up equation for the number of baskets made: 41=x+y. Set up equation for the number of points scored: 92=2x+3y.
A shipping company is shipping cargo by truckloads. The number of miles per gallon the truck averages goes down as the weight of each load goes up.
Find the interval(s) on which f(x) increases, given that f(x) = x3 - 12x + 1. Find the interval(s) on which f(x) increases, given that f(X) =- 2x (25x2 + 75 + 72).
Solve the equations by using addition or substitution method.
Solve the following inequality problems. You must give your answer using the interval notation. You must also give you answer in graphical form (using the number line).
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