New posts in abstract-algebra

How to compute the Galois group of $x^5+99x-1$ over $\mathbb{Q}$?

Finding a permutation, and number of, from powers of the permutation

Primes inert in quadratic field of class number one

Quaternions as an Algebra

Nilpotent elements in $\mathbb{Z}_n$

what is the meaning of the notation $f: A\times B \rightarrow C$

For a field $K$, is there a way to prove that $K[x]$ is a PID without mentioning Euclidean domain?

Isomorphism of $S^1$.

Rational function field over uncountable field is uncountably dimensional

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 $x^2+ax+1=0$

Prove that $n$ divides $\phi(a^n-1)$, where $\phi$ is Euler's $\phi$-function.

Arithmetic structure including both unique factorization and Dedekind domains

To find all integers $n > 1$ for which $(n-1)!$ is a zero-divisor in $Z_n$.

What's the intuition behind a split exact sequence?

Which group of order 24 is this group?

The maximum order of the elements of a group and the number of elements that have that order

Same minimal polynomial gives isomorphism

Is a completion of an algebraically closed field with respect to a norm also algebraically closed?

Is the quotient of a complete ring, complete?

Exercise with Nakayama's lemma