abstract algebra - $K$ is a splitting field $\iff$ any irreducible ...
Let K/F K / F be a finite extension. I want to show that K K is a splitting field over F F any irreducible polynomial p(x) ∈ F[x] p (x) ∈ F [x] that has a root in K K splits completely over K K. I haven't even …
abstract algebra - If $G/Z (G)$ is cyclic, then $G$ is abelian ...
@Robert: Yes, I think so. Where did the negative exponent come from? Would you want to make this comment a formal "answer"?
Integrated Circuit: Definition, Formula, Derivation and Examples - Toppr
An integrated circuit refers to a chip that contains various interconnected multiple electronic components. Furthermore, the location of this chip is on a semiconductor material and it contains …
If $φ:I→J$ is a homeomorphism then $f_n→f$ implies that $ (f_n∘φ) → …
Jan 8, 2022 · If $φ:I→J$ is a homeomorphism then $f_n→f$ implies that $ (f_n∘φ) → (f∘φ)$ with respect the uniform, pointwise and $L_2$ topology respectively?
Show that if $g \\circ f$ is injective, then so is $f$.
May 10, 2015 · The Problem: Let X, Y, Z X, Y, Z be sets and f: X → Y, g: Y → Z f: X → Y, g: Y → Z be functions. (a) Show that if g ∘ f g ∘ f is injective, then so is f f. (b) If g ∘ f g ∘ f is surjective, must g g be …
radicals - Is there a way to check if an integer is a square ...
Nov 11, 2019 · Is there a way to check if a number is square number? For example, we know that 4 4 is a square number because 22 = 2 2 2 = 2 and 9 9 is a square number because 32 = 9 3 2 = 9. But for …
Mutually Singular measures - Mathematics Stack Exchange
(ii) $\int_Ig_ndm=1$ for all $n$, (iii) $\lim_ {n\to\infty}\int_Ifg_ndm=\int_Ifd\mu$ for every $f\in C (I)$. Does it follow that the measures $\mu$ and $m$ are mutually singular? I know that $\mu$ and $m$ …
Two Circles intersecting, common tangent: Proof $GI=IH$
Thanks for the link, but unfortunately I'm looking for a proof with triangles, congruences and so on.
If $f$ and $g$ are surjective, then $g (f (x))$ is surjective
Sep 25, 2016 · What part of the proof are you having trouble understanding? In my reading, the image you posted contains a complete and detailed proof directly from the definition of surjective.
If x is rational, $x\ne 0$, and $y$ irrational, prove $x+y, x-y, xy, x ...
Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, …