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Commutative-algebra
New post in Commutative-algebra
Structure theorem of Artinian rings
November 7th, 2022
ring-theory
commutative-algebra
Prove that if $R$ is a principal ideal ring and $S$ is a multiplicatively closed subset of $R$ then $S^{-1}R$ is also a principal ideal ring.
August 1st, 2022
commutative-algebra
ring-theory
Codimension and Krull's principal ideal theorem
June 11th, 2020
commutative-algebra
algebraic-geometry
Is the map $f^*: \mathrm{Spec}(S) \to \mathrm{Spec}(R)$ injective or surjective where $f: R \to S$ is a ring homomorphism.
September 1st, 2020
abstract-algebra
commutative-algebra
maximal-and-prime-ideals
Is the coordinate ring $\mathbb{C}[x,y]/(x^2+y^2-1)$ or the ring $\mathbb{C}[t,t^{-1}]$ unique factorization domains?
August 1st, 2022
abstract-algebra
unique-factorization-domains
commutative-algebra
If every prime ideal in a ring $R$ is finitely generated, then $R$ is Noetherian?
August 1st, 2022
abstract-algebra
commutative-algebra
ideals
noetherian
When is the localization map injective?
August 1st, 2022
localization
ring-theory
abstract-algebra
commutative-algebra
definition of the grade of an ideal
August 1st, 2022
commutative-algebra
Tensor product of the fraction field of a domain and a module over the domain
November 10th, 2020
tensor-products
commutative-algebra
What does the shifting of graded modules mean here?
August 1st, 2022
graded-modules
commutative-algebra
Irreducible components in the spectrum of a ring
August 1st, 2022
algebraic-geometry
commutative-algebra
Finding Radical of an Ideal
August 1st, 2022
algebraic-geometry
ideals
commutative-algebra
Field of fractions of integral extension is an algebraic extension
April 12th, 2020
integral-extensions
field-theory
abstract-algebra
commutative-algebra
the intersection of maximal ideal
August 1st, 2022
ring-theory
commutative-algebra
maximal-and-prime-ideals
abstract-algebra
Noetherian ring of Krull dimension $0$
April 28th, 2020
ideals
commutative-algebra
abstract-algebra
ring-theory
Localization of a direct product
August 1st, 2022
ring-theory
abstract-algebra
noncommutative-algebra
commutative-algebra
Steps in Finding the Multiplicity of a Point in a Projective Curve
October 11th, 2020
algebraic-geometry
commutative-algebra
Artin local ring
December 2nd, 2020
abstract-algebra
commutative-algebra
If $p$ is a prime ideal then $p[X]$ is a prime ideal
July 2nd, 2020
commutative-algebra
Zero divisors, nilpotents and units in the ring of functions $\mathbb{R} \to \mathbb{R}$
September 1st, 2020
commutative-algebra
ring-theory
Spectrum of a localized ring
August 16th, 2020
commutative-algebra
Let A a commutative ring with unity in which every element is idempotent ($x^n=x$ for some n>1 dependent on x), then every prime ideal is maximal.
August 1st, 2022
commutative-algebra
abstract-algebra
Is a finitely generated torsion module over PID an injective module?
August 1st, 2022
abstract-algebra
commutative-algebra
modules
Finitely Presented Modules Definition
August 1st, 2022
commutative-algebra
modules
abstract-algebra
What does Hom(M,N) mean? Atiyah Macdonald proposition 2.9
June 1st, 2020
abstract-algebra
commutative-algebra
exact-sequence
modules
$R[x]$ has a subring isomorphic to $R$.
August 1st, 2022
ring-theory
polynomials
commutative-algebra
abstract-algebra
Question regarding to Dedekind domain and PID
August 1st, 2022
algebraic-number-theory
commutative-algebra
Maximal Ideals of $\mathbb C[x, y]$
October 27th, 2020
commutative-algebra
abstract-algebra
algebraic-geometry
ring-theory
maximal-and-prime-ideals
Scalar operators and commutators
August 1st, 2022
commutative-algebra
operator-algebras
Basis of a subset of finitely generated torsion-free module
August 1st, 2022
modules
abstract-algebra
commutative-algebra
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