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New posts in abstract-algebra
How to compute the Galois group of $x^5+99x-1$ over $\mathbb{Q}$?
abstract-algebra
field-theory
galois-theory
Finding a permutation, and number of, from powers of the permutation
abstract-algebra
group-theory
permutations
Primes inert in quadratic field of class number one
abstract-algebra
algebraic-number-theory
Quaternions as an Algebra
abstract-algebra
quaternions
Nilpotent elements in $\mathbb{Z}_n$
abstract-algebra
ring-theory
commutative-algebra
what is the meaning of the notation $f: A\times B \rightarrow C$
linear-algebra
abstract-algebra
functions
vector-fields
function-fields
For a field $K$, is there a way to prove that $K[x]$ is a PID without mentioning Euclidean domain?
abstract-algebra
ring-theory
Isomorphism of $S^1$.
abstract-algebra
complex-analysis
group-theory
ring-theory
Rational function field over uncountable field is uncountably dimensional
linear-algebra
abstract-algebra
field-theory
Number of solns of $x^6+x=a$ in $\mathbb{F}_{2^m}$, where $m\geq 3$ is odd is same as number of solns of $x^2+ax+1=0$
abstract-algebra
polynomials
field-theory
galois-theory
finite-fields
Prove that $n$ divides $\phi(a^n-1)$, where $\phi$ is Euler's $\phi$-function.
abstract-algebra
number-theory
elementary-number-theory
divisibility
totient-function
Arithmetic structure including both unique factorization and Dedekind domains
abstract-algebra
ring-theory
integral-domain
unique-factorization-domains
dedekind-domain
To find all integers $n > 1$ for which $(n-1)!$ is a zero-divisor in $Z_n$.
abstract-algebra
ring-theory
What's the intuition behind a split exact sequence?
abstract-algebra
modules
Which group of order 24 is this group?
abstract-algebra
group-theory
finite-groups
The maximum order of the elements of a group and the number of elements that have that order
abstract-algebra
group-theory
finite-groups
Same minimal polynomial gives isomorphism
abstract-algebra
solution-verification
Is a completion of an algebraically closed field with respect to a norm also algebraically closed?
abstract-algebra
field-theory
normed-spaces
banach-spaces
Is the quotient of a complete ring, complete?
abstract-algebra
commutative-algebra
ring-theory
Exercise with Nakayama's lemma
abstract-algebra
commutative-algebra
modules
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