2. In the following item an extension field L/K is given. Find the degree of the extension and also find a basis a. K=Q, L= Q(√2, √-1) b. K=Q, L= Q(√2, √-1) c. K = Q, L= Q(√2, √3, √5) OSŤ

Q: Show that the cubic field generated by a root of f(x) = 3x2 base. Use the fact that…

A: From the given information. The function f(x) is as follows.

Q: やthe ring KLx,り,z3 wherc K is a field. Prove (x2 - (y1)) that is a K[x, り,そI . Prime ideal of

A: Given:- Ring  K[x ,y ,z]   where k is a field. To Prove:-  [x z-(y2+1)]

Q: Prove that: Using Cauchy's Residue Theorem dz = 1+z² 8

A:

Q: Determine if R is a field an integral domain a unital ring for R=Z/15Z, R=Z/16Z, R=Z/17Z

A:

Q: Find the degree and a basis of the extension field Q(v3, v7) Q(V3 + v7). over

A: This question is from field theory's topic extension of field. Solution is given below.

Q: Using cartesian coordination system only. No curvilinear coordination system allowed. 4. If a scalar…

A:

Q: .55. (+) Let F be a field consisting of exactly three elements 0, 1, x. Prove that +x= 1 and that x…

A:

Q: Prove that √2+1 = 2√√(2) using √z = t²-1 et dt

A:

Q: 1. (a) Using index notation, prove the identity where A is a general vector field. (b) Using index…

A: As per policy we are allowed to solve first three sub-parts of the question. So, I am answering the…

Q: Let 2={1,2,3,4,5,6}. Construct the minimal field containing 1. 8={{1,2}, {3,4}}

A: This is a problem of measure theory.

Q: 15. If S1 and S2 are two semialgebras of subsets of 2, show that the class S1S2 := {A1A2 : A1 € S1,…

A:

Q: Problem of the Week: Consider the vector field F = (P,Q) = ( , -y 1. Show that OP he aQ Əx · 2. Show…

A:

Q: 1. This question concerns the field F(x, y) = (2, -x). a) Plot field F in the window [-3, 3] x…

A:

Q: Show that if and ßz are two Borel fields, then ß1 N B2 is also a Borel field.

A: Given that β1 and β2 are two Borel fields,we have to show that β1∩β2 is also Borel field

Q: H.w Pind the ro.t when [!,3} by Disection?

A: We have to find the root using Bisection method.

Q: Vx(av) = Vaxv+a (Vxv) V (aT) = Va T+a(V.T) V(v⋅w) = (Vv). w + (Vw). v

A: ∇×αv=∇α×v+α(∇×v) Proof: ∇×αv=∑i∂∂x×αv=∑i∂∂x×αv…

Q: Find the divergence of the field F. F= -7x⁶i-5xyj-5xzk

A:

Q: 9. Use the field norm to show: a) 1+/2 is a unit in Z [/2] b) -1+v-3 is a unit in Z [1+-3 ]

A: Use the field norm to show thata1+2 is a unit in 2.b-1+-32 is a unit in -1+-32.

Q: -et Cos wot Z a tj w 2 t Wo

A: We have to use Fourier transform formula.

Q: What is the degree u = of the specified eement 33, F= Q (√3) u Over the Field F?

A:

Q: iven that use the bhi tzS to compute %3D irst shifting Theorem [e"e cos 7+]

A: