Let $K/F$ be a finite extension. I want to show that $K$ is a splitting field over $F$ $\iff$ any irreducible polynomial $p (x)\in F [x]$ that has a root in $K ...

@Robert: Yes, I think so. Where did the negative exponent come from? Would you want to make this comment a formal "answer"?

Nov 11, 2019 · Is there a way to check if a number is square number? For example, we know that $4$ is a square number because $2^2=2$ and $9$ is a square number because $3^2=9$. But for example …

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 …

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?

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.

(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 $m$ …

Sep 13, 2023 · The empty set is a subset of every set including itself, but it is not necessarily an element of any particular set.

May 10, 2015 · @:G. Sassatelli ,here is my approach for part b)please correct me if i am wrong $\text {Assume that }\,\, x\epsilon X\,,y\epsilon Y\,,z\epsilon Z\,\,. \text {As}\, g ...

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, …