Show that {a + b√3 | a, b ∈ Q} is a field (a subfield of...

Show that {a + b√3 | a, b ∈ Q} is a field (a subfield of the field R), but {a + b√3 | a, b ∈ Z} is not a field.

Expert Solution

Colby Messinger answered 1 year ago

Show that the quotient ring Q[x]/(x2 − 3) is isomorphic to a subfield of the real...

Show that the quotient ring Q[x]/(x2 − 3) is isomorphic to a subfield of the real numbers R.

(a)Show that S = {a+b √ 5 | a, b ∈ Q} is a subring of...

(a)Show that S = {a+b √ 5 | a, b ∈ Q} is a subring of the real numbers (with the usual + and × of real numbers). Explain why S is a field. (b) Prove that if r is an element of a ring R and r 3 = 0, then 1 − r is a unit in R. (c) Write down all the nilpotent elements of Z24, stating the index of nilpotence in each case. Verify the statement...

solve for q in 4000 + 10q^2-q^3 show calculation.

3. Show that the Galois group of (x2 − 3)(x2 + 3) over Q is isomorphic...

3. Show that the Galois group of (x2 − 3)(x2 + 3) over Q is isomorphic to Z2 × Z2. 4. Let p(x) be an irreducible polynomial of degree n over a finite field K. Show that its Galois group over K is cyclic of order n.

let Q(sqrt(2),sqrt(3)) be the field generated by elements of the form a+bsqrt(2)+csqrt(3)+dsqrt(6) where a,b,c,d are in...

let Q(sqrt(2),sqrt(3)) be the field generated by elements of the form a+bsqrt(2)+csqrt(3)+dsqrt(6) where a,b,c,d are in Q(sqrt(2),sqrt(3)) is a vector space of dimension 4 over A. find a basis for Q(sqrt(2),sqrt(3))

Python 3 Fix this: show the current date where the calendar field is # required library...

Python 3 Fix this: show the current date where the calendar field is # required library import tkinter as tk from tkcalendar import DateEntry import xlsxwriter # frame window = tk.Tk() window.title("daily logs") #window.resizable(0,0) # labels tk.Label(window, text="Bar code").grid(row=0, sticky="W", pady=20, padx=20) tk.Label(window, text="Products failed").grid(row=1, sticky="W", pady=20, padx=20) tk.Label(window, text="Money Lost").grid(row=2, sticky="W", pady=20, padx=20) tk.Label(window, text="Failed date").grid(row=3, sticky="W", pady=20, padx=20) # entries barcode = tk.Entry(window) product = tk.Entry(window) money = tk.Entry(window) # arraging barcode.grid(row=0, column=1) product.grid(row=1, column=1) money.grid(row=2, column=1) cal...

Q.3 (a) Show that in alpha decay from a stationary parent nuclide that the conservation of...

Q.3 (a) Show that in alpha decay from a stationary parent nuclide that the conservation of energy and momentum lead to a relation between the decay energy for the nuclear reaction and the kinetic energy gained by the alpha particle, KE, given by Q = KE(1+ 1m(daughter ) × m(42He)) What is the velocity of the alpha particle emitted in the decay of 238U?. Given Q = 4.28 MeV, mα = 4.0015u, mdaughter = mthorium = 233.99409u 10 (b) Draw...

Show work for both the questions 1) a. Cost of field servicing 50 b Product testing....

Show work for both the questions 1) a. Cost of field servicing 50 b Product testing. 180 c. Inspection of goods. 60 Rework labor and overhead. 62 Downtime caused by defects. 159 f Depreciation of test equipment. 40 Net cost of scrap 45 Quality circles. 83 Field testing at customer site 136 Statistical process control. 278 Technical support to suppliers. 27 Product recalls 30 Quality engineering 50 What is the total appraisal costs? A. $ 285 B $ 421 C...

(a) Use Gauss’s Law for the electric field to show that the electric field is discontinuous...

(a) Use Gauss’s Law for the electric field to show that the electric field is discontinuous at the charged surface of a conducting plane. (b) Devise a way to apply this same approach to a patch on a charged spherical conductor. Hint: Draw a diagram with the electric field so you can specify the shape of the surface.

This is for an electric field mapping lab. Show that electic field strength is equal to...

This is for an electric field mapping lab. Show that electic field strength is equal to the potential gradient.

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