<we><edit> <!-- questions and answers -->
modules
exponential-function
vector-spaces
reference-request
convex-analysis
algebraic-geometry
field-theory
discrete-mathematics
hilbert-spaces
linear-transformations
euclidean-geometry
finite-groups
geometry
riemannian-geometry
algorithms
binomial-coefficients
permutations
set-theory
limits
trigonometry
proof-writing
differential-topology
linear-algebra
prime-numbers
complex-numbers
abstract-algebra
Hilbert scheme of $n$ point action, torus action fixed points
abstract-algebra
combinatorics
monomial-ideals
Is $\mathbb{R}[x]/(x^2+1) \cong \mathbb{C}$?
abstract-algebra
Does anyone know a simple proof for the fundamental theorem of finitely generated abelian group?
abstract-algebra
group-theory
modules
abelian-groups
Problem of invariants of binary forms of degree $d$
abstract-algebra
commutative-algebra
Another proof for Cayley-Hamilton theorem for modules by means of induction on the number of generators
abstract-algebra
induction
modules
Factor of polynomial ring
abstract-algebra
polynomials
ring-theory
If $A[X] \cong B[X]$ as rings, are the degrees of irreducible polynomials the same in $A$ and in $B$?
abstract-algebra
polynomials
ring-theory
irreducible-polynomials
K is a subgroup of G. Determine whether the given cosets are disjoint or identical
abstract-algebra
group-theory
quotient-group
The multiplicative group $ \mathbb {{F}^{\times}_{7}}$ is isomorphic to a subgroup of multiplicative group $ \mathbb {{F}^{\times}_{31}}$
abstract-algebra
group-theory
group-isomorphism
An Example in Finite Group Theory
abstract-algebra
group-theory
finite-groups
Is this a valid proof for why all modules over a field are projective?
abstract-algebra
vector-spaces
field-theory
modules
projective-module
How to find closed form or numerical solution to general power fit equation?
abstract-algebra
numerical-methods
algebraic-number-theory
Statements about normal operator
abstract-algebra
operator-theory
hilbert-spaces
Finding all unitary ring homomorphisms
abstract-algebra
ring-theory
Proof that an automorphism of an extension field of $\mathbb Q$ fixes rationals
abstract-algebra
galois-theory
Why is the algebra product $A\otimes A\to A$ well defined, given that we know the product $A\times A\to A$?
linear-algebra
abstract-algebra
True or False: For any transposition $(a, b) \in S_p$ such that $1 \le a < b \le p$, it follows that $(b-a, p) = 1$.
abstract-algebra
group-theory
symmetric-groups
Ideal class group of $ \mathbb{Z}[ \sqrt{2} ] $
abstract-algebra
principal-ideal-domains
dedekind-domain
Explicit concrete examples of k-affinoid algebras
abstract-algebra
commutative-algebra
norm
valuation-theory
algebras
Prove that a finite abelian group contains an element of order $m$ if and only if $m$ divides $n_1$.
abstract-algebra
group-theory
finite-groups
About roots for 5 degree polynomial
abstract-algebra
If $G$ is a group of order $p^5,$ is $C_G(g)$ a normal subgroup of $G,$ where $g \in G \setminus G^{'}.$
abstract-algebra
finite-groups
What specific algebraic properties are broken at each Cayley-Dickson stage beyond octonions?
abstract-algebra
complex-numbers
quaternions
octonions
sedenions
Question has fallen in Net-JRF exam?
abstract-algebra
group-theory
abelian-groups
Are the groups $\mathbb C^\times \times \mathbb R^ \times$ and $\mathbb R^ \times\times \mathbb R^ \times$ isomorphic?
abstract-algebra
group-theory
abelian-groups
group-isomorphism
infinite-groups
Degree of field extensions in $\mathbb{Q}$ with two algebraic elements
abstract-algebra
field-theory
extension-field
isomorphism of two semigroups
abstract-algebra
semigroups
Problem 20 from Herstein's book
abstract-algebra
group-theory
proof-verification
Generators of a simple extension K over F
abstract-algebra
field-theory
What is a necessary condition to form a set of basis?
linear-algebra
abstract-algebra
Prove that if in ring $R$ multiplications $xy$ and $yx$ are invertible, then elements $x$ and $y$ are also invertible.
abstract-algebra
ring-theory
A question on maximal subgroups of a finite group.
abstract-algebra
group-theory
finite-groups
Irreducible factors of polynomial $X^{p^n}-X$ over $\mathbb{F}_{p^i}[X]$
abstract-algebra
finite-fields
irreducible-polynomials
How many surjective homomorphisms from $\mathbb{Z}^2$ to $\mathbb{Z}/3\mathbb{Z}$?
abstract-algebra
group-theory
$G$ has a copy of $G/N$
abstract-algebra
group-theory
normal-subgroups
quotient-group
G is a group and H is a subgroup of G. Find the index of...
abstract-algebra
Prove that in a Euclidean domain $R$, if a condition is satisfied then $x$ is a unit
abstract-algebra
Is $1+2\sqrt{-2}$ an irreducible element of $\mathbb{Z}[\sqrt{-2}]$? Is it prime?
abstract-algebra
ring-theory
Testing a polynomial's reducibility
abstract-algebra
irreducible-polynomials
Show that a certain quotient is indecomposable
abstract-algebra
representation-theory
Prove these subrings are ideals
abstract-algebra
ring-theory
ideals
Proving formula involving Euler's totient function
abstract-algebra
number-theory
elementary-number-theory
totient-function
Find two subrings S and T such that S + T is not a subring
abstract-algebra
The alternating group An
abstract-algebra
group-theory
Describe all prime and maximal ideals of $\mathbb{Z}_n$
abstract-algebra
ring-theory
ideals
Are there algebraic objects in which "associativity" holds only up to some finite $n$?
abstract-algebra
binary-operations
Difference between algebraic semantics and algebraization of a logic
abstract-algebra
logic
first-order-logic
Rules for divisibility based on digit sum in general basis.
abstract-algebra
algebra-precalculus
elementary-number-theory
modular-arithmetic
Identify the ring $\mathbb {Z}[i]/(2 + i) $
abstract-algebra
ring-theory
ring-isomorphism
spin projector in inverted matrix
linear-algebra
abstract-algebra
physics
inverse
Is there a group containing two subgroups: H with 6 elements and K with 10, such that $|H\cap K| = 1$?
abstract-algebra
Isomorphism between field and polynomial ring over the field
abstract-algebra
polynomials
ring-theory
Proving irreducibility
abstract-algebra
algebraic-geometry
irreducible-polynomials
Is a subrepresentation just a subspace, or a representation itself?
abstract-algebra
group-theory
representation-theory
definition
Let A be an $m \times n$ matrix, using matrix algebra prove that
linear-algebra
abstract-algebra
matrices
Let $f(x)=x^3+x^2+1$ be a cyclotomic polynomial in $Z[x]$? is it a maximal Ideal??
abstract-algebra
polynomials
ideals
List all equivalence classes of associate elements of $\mathbb{Z}_{12}$
abstract-algebra
ring-theory
Claim in polynomial division in $R[x,y]$
abstract-algebra
polynomials
ring-theory
irreducible-polynomials
Can this be considered as an operation over a quotient ring?
abstract-algebra
ring-theory
finite-fields
In which of the cases $F = \mathbb{Z}_2$ or $F = Q$ the quotient ring $F[x]/(x^2+3)$ is a field
abstract-algebra
Prove that any element of this group ring is an associate to an element of the polynomial ring and that the group ring is an integral domain
abstract-algebra
ring-theory
integral-domain
polynomial-rings
Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$
abstract-algebra
ring-theory
ideals
Number of elements in the quotient ring $\mathbb{Z}_6 [x]/\langle 2x +4\rangle$
abstract-algebra
polynomials
ring-theory
Ring $\frac{\mathbb{Z}}{ \mathbb{6Z}}[x] / \langle 2x+4 \rangle\cong\ ?$
abstract-algebra
ring-theory
For this ring homomorphism, show that $\ker f$ is a principal ideal and find an element that generates it
abstract-algebra
ring-theory
ring-homomorphism
Can I prove some thing about dihedral group in term of it subgroup of permutation group?
abstract-algebra
group-theory
proof-writing
What is the result of effecting permutation $(124)$ on $\{1, 2, 3, 4, 5, 6\}$?
abstract-algebra
functions
permutations
If $Gal(f/\mathbb{Q}) \cong S_n$ then $Gal(f/\mathbb{Q}(\alpha_1)) \cong S_{n-1}$?
abstract-algebra
group-theory
field-theory
galois-theory
separable-extension
If every prime ideal is maximal, what can we say about the ring?
abstract-algebra
ring-theory
Commutator subgroup of finite $p$-group of order $p^{n}$ with nilpotency class $n-1.$
abstract-algebra
finite-groups
How to show that these derived functors are equivalent?
abstract-algebra
category-theory
modules
homological-algebra
derived-functors
the number of roots of $f∈R[x]$(R is integral domain) is at most n
abstract-algebra
ring-theory
Given $C$ a field, $f$ a polynomial in $C[x]$ and $I = (f)$, describe $C[x]/I$
abstract-algebra
polynomials
A semigroup in which both the equations ax=b and ya=b have unique solution, is a group. Prove it.
abstract-algebra
proof-verification
semigroups
Help With Proof of Theorem 1.A. in "Topics in Algebra"
abstract-algebra
elementary-set-theory
equivalence-relations
Finding equivalent submodular function
abstract-algebra
geometry
algorithms
real-numbers
modular-function
Inverse of a Particular Matrix help R-{0}
linear-algebra
abstract-algebra
matrices
algebra-precalculus
Is $\alpha=3-\sqrt[5]{5}-\sqrt[5]{25}$ algebraic over $\mathbb{Q}$?
abstract-algebra
field-theory
Prove that there is unique group of order 35 up to isomorphism
abstract-algebra
group-theory
How to compute the abelian group $\text{Ext}_{\mathbb{Z}}^{n}(\mathbb{Z} / {a}\mathbb{Z} , \mathbb{Z} / b{\mathbb{Z}})$?
abstract-algebra
commutative-algebra
homological-algebra
abelian-groups
Definition of equivalence of polynomial under a F[x] where is F is a field.
abstract-algebra
ring-theory
Rational canonical form of diagonal matrix
linear-algebra
abstract-algebra
free-modules
Should I take Real Analysis and Abstract Algebra together?
real-analysis
abstract-algebra
education
advice
Prve that $x^4+x^2+x+1$ is irreducible over $\mathbb{Q}$.
abstract-algebra
polynomials
ring-theory
Prove that a group of order $132=11\cdot 12$ has a normal subgroup of order 11 or a normal subgroup of order 12.
abstract-algebra
group-theory
sylow-theory
Are all polynomials of degree 1 irreducible?
abstract-algebra
polynomials
ring-theory
Classification of cyclic Galois extensions
abstract-algebra
field-theory
galois-theory
galois-extensions
Is maximal unramified extension with a lifting of the residue field fixed under automorphism?
abstract-algebra
commutative-algebra
valuation-theory
Describe all abelian groups of order 24 up to isomorphism
abstract-algebra
If $K$ is a field, prove the polynomial ring $K[x]$ has infinitely many maximal ideals.
abstract-algebra
polynomials
ring-theory
Showing that $\mathbb{D}=\{ \frac{p}{10^n}\mid p \in \mathbb{Z}, n \in \mathbb{N} \}$ is a principal ideal domain.
abstract-algebra
ring-theory
principal-ideal-domains
Prove that an ideal in $C[x]$ is a max ideal
abstract-algebra
ring-theory
complex-numbers
ideals
Functions on a cover with the property $f(U \cap V) = f(U)\,f(V)$
abstract-algebra
general-topology
reference-request
semigroups
semigroup-homomorphism
Find the sum and product of $f(x)=3x-5, g(x)=2x^2-4x+3$ in $Z_8$.
abstract-algebra
polynomial-rings
I want to prove that there is a group $G$ of order $p^{3}$ satisfying $|a|=p^{2},\,|b|=p \,and\, b^{-1}ab=a^{1+p}$
abstract-algebra
sylow-theory
Group rings of elementary Abelian p-groups over finite fields
abstract-algebra
finite-groups
finite-fields
abelian-groups
A problem of central simple algebras: why $(E,s,\gamma)\cong M_n(F)$ only if $\gamma$ is the norm of an element of $E$?
abstract-algebra
ring-theory
representation-theory
noncommutative-algebra
semi-simple-rings
If $G$ is a non-abelian group of order $p^{3}$ for prime p , then the center of $G$ is generated by all elements of the form $aba^{-1}b^{-1}.$
abstract-algebra
sylow-theory
Action of $SL_2\left(\mathbb{Z}\right)$ on $\mathbb{RP}^1$ is minimal
abstract-algebra
group-theory
analysis
group-actions
projective-space
Understanding Quotient of a Quotient Ring
abstract-algebra
quotient-spaces
polynomial-rings