New posts in abstract-algebra

Characteristic of an integral domain must be either $0$ or a prime number.

Order of element of a cyclic group proof [duplicate]

Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$ [duplicate]

$\bar{\mathbb{F}}_p$ is not a finite degree extension of any proper subfield.

Vandermonde identity in a ring

Principal ideal rings that are not integral domains

Is this structure a group?

Are two finite groups of the same order always isomorphic?

What is the formal definition of polynomial ring of several variables?

If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$

Isomorphism of Vector spaces over $\mathbb{Q}$

Fundamental Theorem of Algebra: What are two roots for $x^2$?

Lang Lemma 6.1 (before Sylow): if $p$ divides order of finite abelian group, then subgroup with $p$ order exists. Why is $x^s\neq1$ guaranteed?

Can you always find a surjective endomorphism of groups such that it is not injective?

Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?

Whence this generalization of linear (in)dependence?

Algorithms for symbolic definite integration?

Let $M$ be a maximal ideal in $R$ such that for all $x\in M$, $x+1$ is a unit. Show that $R$ is a local ring with maximal ideal $M$

Is there an intuitive proof of the identity $ \sum_{L \subset S} \prod_{x \in L} (x-1) = \prod_{x \in S} x$ from general principles?

Intuition behind Direct limits