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New posts in abstract-algebra
Characteristic of an integral domain must be either $0$ or a prime number.
abstract-algebra
ring-theory
Order of element of a cyclic group proof [duplicate]
abstract-algebra
group-theory
finite-groups
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$ [duplicate]
abstract-algebra
group-theory
elementary-number-theory
cyclic-groups
gcd-and-lcm
$\bar{\mathbb{F}}_p$ is not a finite degree extension of any proper subfield.
abstract-algebra
field-theory
galois-theory
finite-fields
Vandermonde identity in a ring
abstract-algebra
commutative-algebra
polynomials
ring-theory
binomial-coefficients
Principal ideal rings that are not integral domains
abstract-algebra
ring-theory
principal-ideal-domains
integral-domain
Is this structure a group?
abstract-algebra
group-theory
semigroups
Are two finite groups of the same order always isomorphic?
abstract-algebra
group-theory
finite-groups
What is the formal definition of polynomial ring of several variables?
abstract-algebra
polynomials
definition
If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$
abstract-algebra
field-theory
extension-field
Isomorphism of Vector spaces over $\mathbb{Q}$
linear-algebra
abstract-algebra
vector-spaces
Fundamental Theorem of Algebra: What are two roots for $x^2$?
abstract-algebra
algebra-precalculus
polynomials
Lang Lemma 6.1 (before Sylow): if $p$ divides order of finite abelian group, then subgroup with $p$ order exists. Why is $x^s\neq1$ guaranteed?
abstract-algebra
group-theory
finite-groups
abelian-groups
Can you always find a surjective endomorphism of groups such that it is not injective?
abstract-algebra
group-theory
hopfian-groups
Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?
abstract-algebra
commutative-algebra
definition
ideals
Whence this generalization of linear (in)dependence?
abstract-algebra
modules
abelian-groups
Algorithms for symbolic definite integration?
abstract-algebra
definite-integrals
computer-algebra-systems
symbolic-computation
Let $M$ be a maximal ideal in $R$ such that for all $x\in M$, $x+1$ is a unit. Show that $R$ is a local ring with maximal ideal $M$
abstract-algebra
commutative-algebra
Is there an intuitive proof of the identity $ \sum_{L \subset S} \prod_{x \in L} (x-1) = \prod_{x \in S} x$ from general principles?
abstract-algebra
Intuition behind Direct limits
abstract-algebra
commutative-algebra
homological-algebra
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