Results for query " the skew polynomial"

Illustrator: How to skew text independently of path?

So I have some text wrapped around a circle (with the type on a path tool), and from here I'd like to skew the text so it's slanting a bit to the right.However, when I use the skew tool, it skews the entire path that it's on, but I want to skew the text independent of the path.

Skew text in Photoshop without transform

I have a PSD file with a multiline skew text and I need to know how to do the same thing from the scratch.I am not so good at Photoshop, and the only way I know is applying skew transform to the text object.

The rectification of the transpose of a skew tableau?

Suppose the rectification of a skew tableau is a standard tableau, I want to know if the rectification of the transpose of the skew tableau equals to the transpose of the rectification of the skew tableau?If it's right, how to prove it?

Local rings with simple radical

Is there a (finite) non-commutative local ring $R$ (containing identity) such that $J(R)$ is simple as a left module?For a finite field $k$ with non-trivial automorphism $\sigma$, take the skew polynomial ring $k[X, \sigma]$ (reminder: these are polynomials with coefficients on the left $\sum a_i X^i$ with relation $Xa = \sigma(a)X$) and set $R := k[X, \sigma] / \langle X^2 \rangle$ (i.

Algebraic integers in skew fields

Hi everyone,

let $D$ be a skew field, which is finite dimensional over its center $k$.Assume that $k$ is a number field, and let $\mathcal{O}_D$ be the set of elements $z\in D$ which are roots of a monic polynomial with coefficients in $\mathcal{O}_k$.

Global dimensions of non-commutative rings

Moreover, are there any standard way to compute $gl\dim(S)$ when $S$ is non-commutative?Then let $\sigma_1$ be the $k$-algebra automorphism of $R_1$ defined by $\sigma_1(x_1) = a_{21} x_1$, and let $R_2$ be the skew-polynomial ring
R_2 = R_1[x_2; \sigma_1].

Detecting if a polynomial is a Pfaffian

The pfaffian can be defined as $\sqrt{{\rm det}(A) } $ when $A$ is skew symmetric, or explicitly $${\rm pf}(A) = \frac{1}{2^n n!Let $F \in k[x_0, \ldots, x_n ]$ be a homogeneous polynomial of degree $d$.

Skew polynomial algebra

When I was a very little hare, a big grey wolf told me about the following skew polynomial algebra, which I never understood.My question is whether the following construction is a part of some bigger abstract construction and whether it is been written anywhere.

Square root of the determinant of AB+I where A, B are skew-symmetric

Imagine I have two skew-symmetric square matrices $A$, $B$.) Now I am interested in the square root of the determinant of $AB+I$, where $I$ is the identity matrix,

$$ x = \sqrt{ \det \left( AB + I \right) } $$

As quick inspection for small matrices suggests that this $x$ is a polynomial of the elements of $A$ and $B$, for example for $3 \times 3$ matrices we find

$$ x = 1 - a_{12} b_{12} - a_{13} b_{13} - a_{23} b_{23} $$

and I checked this analytically for matrices up to $6 \times 6$.

On Skew-hermitian and inverse

If $A$ is skew-symmetric real under what conditions do we have $(I+A)^{-1} {'}=I-A$ where $'$ stands for transpose?If $A$ is skew-hermitian complex under what conditions do we have $(I+A)^{-1} {'}=I-A$ where $'$ stands for conjugate transpose?

Almost skew polynomial ring an integral domain?

Since Ore extensions of domains are Ore extensions, this question can be reformulated as follows: Since the relation look almost like those of a skew polynomial ring, can this ring in fact be written as a skew polynomial ring?Consider the $k$-algebra $R=k\langle x_i, c_i\rangle_{i=1,\ldots,n}$, $k$ not of characteristic 2,
subject to the following relations:

$x_ix_j = x_jx_i$ for all $i, j$
$x_ic_i = -c_i x_i$
$x_ic_j = c_j x_i$ for all $i\neq j$
$c_ic_j = -c_j c_i$ for all $i\neq j$

I haven't found a counterexample yet.