Newbetuts
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New posts in abstract-algebra
Adjunctions are Kan Extensions.
abstract-algebra
category-theory
adjoint-functors
If ideal quotients of a ring are isomorphic, are these ideals isomorphic?
abstract-algebra
ideals
Normalizer of a Sylow 2-subgroups of dihedral groups
abstract-algebra
group-theory
finite-groups
sylow-theory
dihedral-groups
Splitting field implies Galois extension
abstract-algebra
field-theory
galois-theory
prove that $\mathbb{C}$ and $\mathbb{R}$ are not isomorphic as rings
abstract-algebra
What is the significance of multiplication (as distinct from addition) in algebra & ring theory?
abstract-algebra
ring-theory
intuition
Characteristic of a simple ring is either prime or $0$
abstract-algebra
ring-theory
Primes of form $a^2 + 24b^2$
abstract-algebra
number-theory
prime-numbers
algebraic-number-theory
Is every commutative ring having the invariant basis number property equivalent to AC?
abstract-algebra
ring-theory
set-theory
modules
axiom-of-choice
Any element of $\mathbf{Z}[\xi]$ is congruent to an integer modulo $(1-\xi)^2$ if multiplied by a suitable power of $\xi$
abstract-algebra
commutative-algebra
algebraic-number-theory
primitive-roots
Graphically Organizing the Interrelationships of Basic Algebraic Structures
abstract-algebra
group-theory
ring-theory
definition
Prove every group of order less or equal to five is abelian [closed]
abstract-algebra
group-theory
abelian-groups
normal-subgroups
Showing $K[u]$ is a field when $u$ is algebraic over $K$.
linear-algebra
abstract-algebra
If M+N and M$\cap$N are finitely generated modules, so are M and N.
abstract-algebra
modules
Understanding of exterior algebra
abstract-algebra
reference-request
exterior-algebra
Finitely generated projective modules are isomorphic to their double dual.
abstract-algebra
projective-module
$2 \otimes_{R} 2 + x \otimes_{R} x$ is not a simple tensor in $I \otimes_R I$
abstract-algebra
modules
tensor-products
Elements of $S_n$ can be written as a product of $k$-cycles.
abstract-algebra
group-theory
permutations
symmetric-groups
permutation-cycles
Why is the quotient map $SL_n(\mathbb{Z})$ to $SL_n(\mathbb{Z}/p\mathbb Z)$ is surjective?
abstract-algebra
group-theory
ring-theory
linear-groups
Minimal polynomial of $\zeta+\zeta^{-1}$
abstract-algebra
field-theory
galois-theory
cyclotomic-polynomials
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