What is the importance of Associated primes of a ring? Does it have many applications in commutative algebra or other fields?
I am interested in applications of Associated primes and its links to other topics in Algebra.
Many Thanks
2026-04-03 06:55:09.1775199309
What is the importance of Associated primes of a ring?
254 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ABSTRACT-ALGEBRA
- Feel lost in the scheme of the reducibility of polynomials over $\Bbb Z$ or $\Bbb Q$
- Integral Domain and Degree of Polynomials in $R[X]$
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Group with order $pq$ has subgroups of order $p$ and $q$
- A commutative ring is prime if and only if it is a domain.
- Conjugacy class formula
- Find gcd and invertible elements of a ring.
- Extending a linear action to monomials of higher degree
- polynomial remainder theorem proof, is it legit?
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
Related Questions in RING-THEORY
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- A commutative ring is prime if and only if it is a domain.
- Find gcd and invertible elements of a ring.
- Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain.
- Prove that $Z[i]/(5)$ is not a field. Check proof?
- If $P$ is a prime ideal of $R[x;\delta]$ such as $P\cap R=\{0\}$, is $P(Q[x;\delta])$ also prime?
- Let $R$ be a simple ring having a minimal left ideal $L$. Then every simple $R$-module is isomorphic to $L$.
- A quotient of a polynomial ring
- Does a ring isomorphism between two $F$-algebras must be a $F$-linear transformation
- Prove that a ring of fractions is a local ring
Related Questions in COMMUTATIVE-ALGEBRA
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- Extending a linear action to monomials of higher degree
- Tensor product commutes with infinite products
- Example of simple modules
- Describe explicitly a minimal free resolution
- Ideals of $k[[x,y]]$
- $k[[x,y]]/I$ is a Gorenstein ring implies that $I$ is generated by 2 elements
- There is no ring map $\mathbb C[x] \to \mathbb C[x]$ swapping the prime ideals $(x-1)$ and $(x)$
- Inclusions in tensor products
- Principal Ideal Ring which is not Integral
Related Questions in IDEALS
- Prime Ideals in Subrings
- Ideals of $k[[x,y]]$
- Product of Ideals?
- Let $L$ be a left ideal of a ring R such that $ RL \neq 0$. Then $L$ is simple as an R-module if and only if $L$ is a minimal left ideal?
- Show $\varphi:R/I\to R/J$ is a well-defined ring homomorphism
- A question on the group algebra
- The radical of the algebra $ A = T_n(F)$ is $N$, the set of all strictly upper triangular matrices.
- Prove that $\langle 2,1+\sqrt{-5} \rangle ^ 2 \subseteq \langle 2 \rangle$
- $\mathbb{Z}[i] / (2+3i)$ has 13 elements
- Ideal $I_p$ in $\mathbb{F}_l[x]/(x^p -1)$ where $\frac{\epsilon p}{2} \leq \dim(I_p) < \epsilon p$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
From what I understand, they provide a refinement of the theory of primary decomposition. Since they are contained in the support of the module, you can localize the module at them and not get a zero module.
I think associated primes are also used to study uniform modules over Noetherian rings.
It also shows up again when defining unmixedness of an ideal in Noetherian rings.