# Tag Info

Accepted

### What is the difference between addition and product in abstract algebra?

This is subtle. You could say that the lesson of abstract algebra is that there is this more fundamental concept of an "operation," and both "addition" and "multiplication&...
Accepted

### Classification of finite groups of order $p^3qr$ up to isomorphism

I suspect there is no complete classification of groups of order $p^3qr$. There is a 2022 paper by Dietrich, Eick and Pan with a complete and detailed classification of group whose orders have at most ...

### Voight's Quaternion Algebras, Corollary 7.1.2

Sorry for not seeing this sooner! There is a major glitch in this argument: if $I \cap I \alpha = \{0\}$, then this does not imply that $I\alpha \subseteq I$! This is just hogwash. But what is true ...

### Does an element of a group to the 0th power equal the identity?

The answer is certainly morally correct. But it might be clearer to say that initially $x^0$ has no meaning, as per group axioms. We must define it. If we define it as $id$ then the original identity ...
Accepted

### Mock scalar product's nonlinearity as a derivation

Here is a proof assuming the characteristic is different from $2$. For convenience of typing I will write $\langle u,v\rangle$ as $(u,v)$. Note first that homogeneity with respect to the scalar $s+t$...
Accepted

### Product ideals are the kernel of what ring homomorphism?

I don't believe there is a way to do this. The natural thing to do with two quotients $R \to R/I_1$ and $R \to R/I_2$ is to consider their product $R \to R/I_1 \times R/I_2$, and of course what this ...
1 vote

### A doubt regarding the extension of Weierstrass factorization theorem

The Weierstraß product theorem is more complicated, it says, that for a set of set zeros and multiplicities ${a_k,n_k}$, without a finite limit point of the postions $a_k$, there exists analytic ...
1 vote

### Applications of Category Theory in Abstract Algebra

There are alot of good reasons to state things categorically. Universal Properties Category theory is made to give a precise meaning to universal properties. I don't think it is possible to ...
1 vote
Accepted

### Surjective ringhomomorphism

Let me go line by line. $\phi(a+b)=\phi((a+b\sqrt{-5})+(c+d\sqrt{-5})) = \overline{a+b+c+d}$ The problem here is that $a+b\neq a+ b\sqrt{-5} + c + d\sqrt{-5}$ in general and what you want to write ...
1 vote
Accepted

1 vote

### Is there a notion of best $\mathbb{K}$-approximations where $\mathbb{K}$ is an algebraic number field?

Similar to how we know that the best $\mathbf Q$-approximations of a given real number $x>0$ are given via the partial fractions of its continued fraction representation It depends on what you ...

Only top scored, non community-wiki answers of a minimum length are eligible