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Taking a break for a while.


1d
revised When is a vector field on a manifold restricted to a submanifold $X$ a vector field on $X$?
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comment When is a vector field on a manifold restricted to a submanifold $X$ a vector field on $X$?
@OlivierBegassat: Of course you are correct.
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asked When is a vector field on a manifold restricted to a submanifold $X$ a vector field on $X$?
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reviewed Close Find the center and radius of polar circle equation
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revised Calculate the tensor product of two vectors
edited tags
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reviewed Close Use mathematical induction to show that
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reviewed Reviewed Example of a Short Exact Sequence
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comment Each element is a square of some element
I suppose that depends on how explicit your description of $\mathbb{F}_{2^n}$ is. One way to do it is to use Martin Brandenburg's approach. If $x^2 = 0$, then $x = x^{2^n} = (x^2)^{2^{n-1}} = 0^{2^{n-1}} = 0$ so $x = 0$.
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reviewed Leave Closed urgent help please solve this eqaution
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reviewed Close Using Taylor series to find $\lim_{x\to 1}\frac{2-(x+3)^{1/2}}{x-1}$
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reviewed Looks OK A Challenge on One Integral Problem
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reviewed Looks OK How many different pairs can I have from two groups?
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comment Each element is a square of some element
The kernel of a ring homomorphism is always an ideal. The only ideals in a field are the zero ideal and the whole field, so $\ker\phi = \{0\}$ or $\ker\phi = \mathbb{F}_{2^n}$. If you can give an example of an element of $\mathbb{F}_{2^n}$ which has non-zero square (e.g. $1$), then $\ker\phi \neq \mathbb{F}_{2^n}$ so we must have $\ker\phi = \{0\}$.
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reviewed No Action Needed Intersection of two hyperplanes
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comment Finding the kernel of $\phi:\Bbb{Z}_6\to\Bbb{Z}_2 $ given by $\phi(x)=$ the remainder of $x$ when divided by $2$
Good. So the kernel of $\phi$ is $\{0, 2, 4\}$.
1d
revised Finding the kernel of $\phi:\Bbb{Z}_6\to\Bbb{Z}_2 $ given by $\phi(x)=$ the remainder of $x$ when divided by $2$
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1d
revised Finding the kernel of $\phi:\Bbb{Z}_6\to\Bbb{Z}_2 $ given by $\phi(x)=$ the remainder of $x$ when divided by $2$
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reviewed Close Why does the following reduction holds?
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answered Finding the kernel of $\phi:\Bbb{Z}_6\to\Bbb{Z}_2 $ given by $\phi(x)=$ the remainder of $x$ when divided by $2$
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reviewed Delete The Stupid Computer Problem : can every polynomial be written with only one $x$?