Newbetuts
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New posts in abstract-algebra
Rig in which 0 is not an absorber.
abstract-algebra
ring-theory
monoid
semiring
Is homotopy group of infinite product of spaces a direct sum or a direct product of groups?
abstract-algebra
algebraic-topology
category-theory
direct-sum
direct-product
Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
abstract-algebra
ring-theory
Using Burnside's Lemma; understanding the intuition and theory
abstract-algebra
group-theory
Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$
abstract-algebra
field-theory
galois-theory
"Classify $\mathbb{Z}_5 \times \mathbb{Z}_4 \times \mathbb{Z}_8 / \langle(1,1,1)\rangle$"
abstract-algebra
group-theory
abelian-groups
If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$ [duplicate]
abstract-algebra
ring-theory
ideals
noetherian
Is there a simple geometric example of unequal left and right cosets?
abstract-algebra
group-theory
soft-question
finite-groups
examples-counterexamples
Show that a semigroup with $aS \cup \{a\} = bS \cup \{b\}$ and $Sa \cup \{a\} = Sb \cup \{b\}$ is a group
abstract-algebra
group-theory
semigroups
Fundamental group of Klein Bottle
abstract-algebra
group-theory
algebraic-topology
fundamental-groups
klein-bottle
Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?
abstract-algebra
field-theory
extension-field
radicals
axiom-of-choice
Construct a field of 25 elements.
abstract-algebra
finite-fields
Prove that an ideal in $k[x,y]$ is a prime ideal [duplicate]
abstract-algebra
polynomials
irreducible-polynomials
What are the semisimple $\mathbb{Z}$-modules?
abstract-algebra
ring-theory
modules
semi-simple-rings
Show that any subgroup of a finitely generated abelian group is finitely generated?
abstract-algebra
induction
abelian-groups
group-presentation
combinatorial-group-theory
Do the isomorphism's of groups form an equivalence relation on the class of all groups?
abstract-algebra
group-theory
Show the direct sum of noetherian R-modules is noetherian.
abstract-algebra
ring-theory
modules
exact-sequence
direct-sum
If A is noetherian, then Spec(A) is noetherian
abstract-algebra
commutative-algebra
ring-theory
Invertibility of elements in a left Noetherian ring
abstract-algebra
ring-theory
noncommutative-algebra
Universal property of the completion of rings / modules
abstract-algebra
commutative-algebra
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