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New posts in abstract-algebra
How do extension fields implement $>, <$ comparisons?
abstract-algebra
extension-field
ordered-fields
If $n\ge m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
abstract-algebra
combinatorics
permutations
symmetric-groups
Is $\operatorname{Hom}_\mathbb{Z}(\mathbb{Q},\mathbb{Q}/\mathbb{Z})\cong\bigoplus_p\mathbb{Q}_p$?
abstract-algebra
homological-algebra
Series with $\zeta$
real-analysis
abstract-algebra
riemann-zeta
Determine the Galois Group of $(x^2-2)(x^2-3)(x^2-5)$
abstract-algebra
field-theory
galois-theory
extension-field
Determining all Sylow $p$-subgroups of $S_n$ up to isomorphism?
abstract-algebra
group-theory
finite-groups
Is $\Bbb Q(\sqrt 2, e)$ a simple extension of $\Bbb Q$?
abstract-algebra
field-theory
extension-field
transcendence-theory
What is meant by a mixed characteristic field?
abstract-algebra
field-theory
Do both versions (invariant and primary) of the Fundamental Theorem for Finitely Generated Abelian Groups hold at the same time?
abstract-algebra
group-theory
ring-theory
modules
abelian-groups
Homology group of $X=\operatorname{SL}(2,\mathbb{R})/\operatorname{SL}(2,\mathbb{Z})$
abstract-algebra
group-theory
algebraic-topology
manifolds
homology-cohomology
What is the deal with the three isomorphism theorems?
abstract-algebra
Presentation of $D_{2n}$
abstract-algebra
group-theory
Number of indecomposable direct summands of $A/AeA$ for a finite dimensional basic algebra $A$ and idempotent $e$
abstract-algebra
modules
representation-theory
Show that $M[x]$ is a Noetherian $A[x]$-module.
abstract-algebra
commutative-algebra
How to describe Algebraic Closure of $\mathbb{C}(x)$?
abstract-algebra
Showing two polynomial rings over $\mathbb{C}$ aren't isomorphic
abstract-algebra
polynomials
ring-theory
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
abstract-algebra
group-theory
finite-groups
How to prove $e^{A \oplus B} = e^A \otimes e^B$ where $A$ and $B$ are matrices? (Kronecker operations)
linear-algebra
abstract-algebra
group-theory
ring-theory
quantum-mechanics
Show that $\mathbb{Q}^+/\mathbb{Z}^+$ cannot be decomposed into the direct sum of cyclic groups.
abstract-algebra
group-theory
Central extensions versus semidirect products
abstract-algebra
group-theory
semidirect-product
group-extensions
central-extensions
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