Linked Questions

Real number is often used to represent a point in a 1-dimensional number line. Real numbers are written as $a$ where $a \in \mathbb{R}$. Complex number is often used to represent a point in a 2-...

As an engineer, I learned a lot about how to use complex numbers. One way I have heard $i$, the unit complex number, defined is: It is orthogonal to the real number line. Because $\frac{\mathrm{d}}{\...

Since there are complex numbers (2 dimensions) and quaternions (4 dimensions), it follows intuitively that there ought to be something in between for 3 dimensions ("triernions"). Yet no one uses ...

Mathematics as a science became richer when Cantor invented the real numbers. Then scientists wanted to solve equations which were not solvable in the real numbers so they invented the complex numbers....

Suppose $R$ is a finite ring (commutative ring with $1$) of characteristic $3$ and suppose that for every unit $u \in R\:,\ 1+u\ $ is also a unit or $0$. We need to show that $R$ is a field. Is this ...

In a ring, $a\neq0$ and $b\neq0$. $aba=0$. Prove $ab=0$ or $ba=0$. This is one question in my abstract algebra homework-- it seems pretty easy at first glance, yet I have spent hours thinking about ...

Is it possible in mathematics to use a third number line based on division by zero; in addition to the real and imaginary number lines? This is because some solutions blow up when there is a division ...

I have been reading about multi-dimensional numbers, and found out that it's been proven that the Octonions are the composition algebra of the largest dimension. I was wondering why, despite having ...

Why is quaternion algebra 4D and not 3D? Complex algebra is 2D and what is known as quaternion algebra jumps to 4D. $ i^2 = j^2 = k^2 = ijk = -1 $ Using $1, i, j,$ and $k$ as the base (where ...

Some time ago I had the idea of extending the real numbers with a new direction/algebraic sign, similarly how negative numbers extend the positive numbers by adding a new sign. I call this sign §, and ...

The question is in the title. By the first isomorphism theorem, I know that if I can find a surjective ring homomorphism $\varphi : \mathbb{R}[x] \rightarrow S$, where $S$ is some standard ring, and ...

I was learning a lot about hypercomplex numbers lately. I've seen articles about complex numbers, double numbers, dual numbers, binarions, quaternions, octonions etc. But one thing in common about all ...

Let A be a commutative algebra of finite dimension, and if $A$ has no nilpotent elements other than $0$, is true that $A \cong \mathbb{C}^n$ ? The question emerge to my mind, I thought that the ...

Give and example of a non-abelian group $(G,.)$ where $a^2b=ba^2\Rightarrow ab=ba$ for all $a,b\in G$. Can somebody give me some tips, please? Moreover how did you think to get there. I've found that ...

On Wikipedia page on vector multiplication, they gave several ways to "multiply" two vectors, the most well known being the dot product and the cross product I am curious whether we can multiply two ...