New posts in abstract-algebra

How do extension fields implement $>, <$ comparisons?

If $n\ge m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.

Is $\operatorname{Hom}_\mathbb{Z}(\mathbb{Q},\mathbb{Q}/\mathbb{Z})\cong\bigoplus_p\mathbb{Q}_p$?

Series with $\zeta$

Determine the Galois Group of $(x^2-2)(x^2-3)(x^2-5)$

Determining all Sylow $p$-subgroups of $S_n$ up to isomorphism?

Is $\Bbb Q(\sqrt 2, e)$ a simple extension of $\Bbb Q$?

What is meant by a mixed characteristic field?

Do both versions (invariant and primary) of the Fundamental Theorem for Finitely Generated Abelian Groups hold at the same time?

Homology group of $X=\operatorname{SL}(2,\mathbb{R})/\operatorname{SL}(2,\mathbb{Z})$

What is the deal with the three isomorphism theorems?

Presentation of $D_{2n}$

Number of indecomposable direct summands of $A/AeA$ for a finite dimensional basic algebra $A$ and idempotent $e$

Show that $M[x]$ is a Noetherian $A[x]$-module.

How to describe Algebraic Closure of $\mathbb{C}(x)$?

Showing two polynomial rings over $\mathbb{C}$ aren't isomorphic

Group homomorphisms and which of the following statements are true (NBHM-$2014$)

How to prove $e^{A \oplus B} = e^A \otimes e^B$ where $A$ and $B$ are matrices? (Kronecker operations)

Show that $\mathbb{Q}^+/\mathbb{Z}^+$ cannot be decomposed into the direct sum of cyclic groups.

Central extensions versus semidirect products