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New posts in ring-theory
Proving $End_A(V) $ is a local ring whose Jacobson -radical is a nil-radical ideal
abstract-algebra
ring-theory
Do the non-units in a commutative ring form an ideal?
abstract-algebra
ring-theory
Show that $(\mathbb{Z}/n)^\times$ cannot be cyclic unless $n$ is either a prime power or twice a prime power.
abstract-algebra
ring-theory
Does every ring with unity arise as an endomorphism ring?
abstract-algebra
ring-theory
abelian-groups
If $A + B = R$ and $A+C=R$ then $A+BC=R$ and $A \cap BC = ABC$
abstract-algebra
ring-theory
ideals
Every non-finitely generated module has a minimal generating set.
abstract-algebra
ring-theory
modules
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
abstract-algebra
ring-theory
Examples of properties not preserved under homomorphism
abstract-algebra
group-theory
ring-theory
big-list
GCD domain is LCM domain
abstract-algebra
ring-theory
Why do we need prime ideals in the spectrum of a ring?
algebraic-geometry
ring-theory
commutative-algebra
solution-verification
What are some examples of vector spaces that aren't graded?
linear-algebra
ring-theory
vector-spaces
Adjoining 1/2 to $\Bbb{Z}/12\Bbb{Z}$
abstract-algebra
ring-theory
$K[x_1, x_2,\dots ]$ is a UFD
abstract-algebra
commutative-algebra
ring-theory
prime-factorization
Quotient Ring with kernel?
abstract-algebra
ring-theory
ideals
Example of non-flat modules
abstract-algebra
ring-theory
modules
flatness
(Simple) Examples on Non-Commutative Rings
discrete-mathematics
ring-theory
Euclidean domain: every irreducible element is prime
abstract-algebra
ring-theory
euclidean-domain
Show that the set generated by $A$ is $\{r_1a_1+r_2a_1+ \dots +r_ka_k \mid k \in \Bbb N, r_i \in R, a_i \in A, i \le k\}.$
abstract-algebra
ring-theory
ideals
Proof that Quaternion Algebras are simple
abstract-algebra
ring-theory
quaternions
Finite ring has only zero divisors and units [duplicate]
abstract-algebra
ring-theory
finite-rings
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