Newbetuts
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New posts in ring-theory
Finite quotient ring of $\mathbb Z[X]$
abstract-algebra
commutative-algebra
ring-theory
finite-rings
Are ideals in rings and lattices related?
ring-theory
order-theory
ideals
lattice-orders
The nil-radical is an intersection of all prime ideals proof
ring-theory
ideals
A direct product of projective modules which is not projective
ring-theory
modules
homological-algebra
projective-module
When is the preimage of prime ideal is not a prime ideal?
ring-theory
Induced map between localizations
abstract-algebra
ring-theory
commutative-algebra
localization
$fg$ primitive $\to$ $f, g$ primitive
abstract-algebra
ring-theory
ideals
Prove that $2$, $3$, $1+ \sqrt{-5}$, and $1-\sqrt{-5}$ are irreducible in $\mathbb{Z}[\sqrt{-5}]$.
abstract-algebra
number-theory
ring-theory
algebraic-number-theory
divisibility
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
abstract-algebra
polynomials
ring-theory
factoring
irreducible-polynomials
direct product commutes with tensor product?
abstract-algebra
ring-theory
modules
tensor-products
Does there exist a ring which is not a principal ideal ring and which has exactly six different ideals?
abstract-algebra
ring-theory
ideals
examples-counterexamples
principal-ideal-domains
Are all subrings of the rationals Euclidean domains?
number-theory
commutative-algebra
ring-theory
principal-ideal-domains
Maximal ideals in $C^\infty(\mathbb{R})$
abstract-algebra
functions
ring-theory
examples-counterexamples
ideals
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
abstract-algebra
ring-theory
ideals
finite-rings
Saturated sets and A-algebras [duplicate]
algebraic-geometry
ring-theory
localization
What is the field of fractions of $\mathbb{Q}[x,y]/(x^2+y^2)$?
abstract-algebra
ring-theory
commutative-algebra
Krull dimension of $\mathbb Z[\sqrt 5]$ and integral ring extensions
abstract-algebra
number-theory
ring-theory
commutative-algebra
Minimal Polynomial of $\sqrt{2}+\sqrt{3}+\sqrt{5}$
abstract-algebra
polynomials
ring-theory
field-theory
minimal-polynomials
$\textbf Z[\sqrt{pq}]$ is not a UFD if $\left( \frac{q}p \right) = -1$ and $p \equiv 1 \pmod 4$. [duplicate]
abstract-algebra
ring-theory
algebraic-number-theory
unique-factorization-domains
A finite commutative ring with the property that every element can be written as product of two elements is unital
abstract-algebra
ring-theory
commutative-algebra
finite-rings
rngs
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