Define φ : Q[x] → Q by φ()
=
.
(a) Prove that φ is a ring homomorphism.
(b) Find the kernel of φ.
We define the ring homomorphism
by
a) Show that the kernel of
is <x3 -2>, and that the image is
b) Conclude that
is a subfield of
SOLVE B only please
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If Y is locally compact Hausdorff space ,prove that there is a homomorphism C(XY,Z)C(X,C(Y,Z)) and define the homomorphism. We were unable to transcribe this imageWe were unable to transcribe this image
10. Define φ : R2 → R by φ(x,y-x + y for (x,y) E R2. Show that φ is an onto homomorphism and find the kernel of φ (10 Points)
Real Analysis: Define f: [0,1] -->
by f(x) = {0, x
[0,1] ; 1, x
[0,1]\
}
(a) Identify U(f) = inf{U(f, P): P
(a,b)}
(b) Prove or disprove that f is Darboux Integrable.
Thanks in advance!
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If
are commutative rings, define their direct product
by induction on
( it is the set of n- tuples (
) with
for all i). Prove that the ring
where
is the set with
is the direct product of
copies of
.
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Let X1,...,X10 be a random sample from N(θ1,1) distribution and let Y1,...,Y10 be an independent random sample from N(θ2,1) distribution. Let φ(X,Y ) = 1 if X < Y , −5 if X ≥ Y , and V= φ(Xi,Yj) . 1. Find v so that P[V>=v]=0.45 when 1=2. 2. Find the mean and variance of V when 1=2. 10 10 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
Let
be a map
Define the map
prove or disprove
2)
for all
3)
for all
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Please show all work:
Let
If x is odd then
If x is even then
Prove that
is true and then solve it.
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(7) In this problem let X denote the vector space C(0, 1) with the sup norm. (a) Given f e X, define d(f) = f2. : X → X is differentiable, and Prove that φ find φ'(f). (b) Given f e X, define 9(f) = J0 [f(t)]2dt. Prove that Ψ : X → R is differentiable. and find Ψ(f).
(7) In this problem let X denote the vector space C(0, 1) with the sup norm. (a) Given f e X,...
Define
, a finite
-group, such that
isn't abelian. Let
such that
, where
is abelian.
Prove that there are either
or
such abelian subgroups, and if there are
, then the index of
in
is
T We were unable to transcribe this imageT K G:K=P We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageT We were unable...