Is the following true?
Assume that $F \leq K \leq M$ are field extensions and $M$ is a Galois extension of $K$ and $K$ is a finite extension of $F$. Is $M$ a Galois extension of $F$?
Assume that you have an n-dimensional vector space over a finite field (therefore the number of elements in the vector space is finite.) and $F$ is a subset of this vector space which contains n nonzero elements that I call "forbidden" elements. Let's $A$ is a subset of this vector space when the...
If $V$ is a vector space over a field $K$, then the symmetric algebra $S(V)$ is defined as the tensor algebra $T(V)$ factorized by the two-sided ideal generated by $x\otimes y-y\otimes x$, with $x,y\in V$. The homogeneous component of degree $n$ of $S(V)$ is $S^n(V)=T^n(V)/I_n$, where $I_n$ is th...
If $V$ is a vector space over a field $K$ then the symmetric algebra $S(V)$ is defined as the tensor algebra $T(V)$ factorized by the two-sided ideal generated by $x\otimes y-y\otimes x$, with $x,y\in V$. The homogeneous component of degree $n$ of $S(V)$ is $S^n(V)=T^n(V)/I_n$, where $I_n$ is the...
I am reading Dale Rolfsen's book KNOTS AND LINKS, at page 115, I can't figure out why the crookedness of a knot equals its bridge index. Please give me some hints or any references avalible, much thanks!
I am reading Dale Rolfsen's book KNOTS AND LINKS, at page 115, I can't figure out why the crookedness of a knot equals its bridge index. Please give me some hints or any references avalible, much thanks!
