I am looking for an example of a local UFD $(R,\mathfrak m)$ of dimension $2$ which is also Gorenstein and $\mathfrak m$ is minimally generated by four elements. Does there exist any such examples?
2026-03-25 06:05:49.1774418749
Examples of Gorenstein local unique factorization domain of dimension $2$ and embedding dimension $4$
77 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 HOMOLOGICAL-ALGEBRA
- How does $\operatorname{Ind}^G_H$ behave with respect to $\bigoplus$?
- Describe explicitly a minimal free resolution
- $A$ - dga over field, then $H^i(A) = 0, i > 1$ implies $HH_i(A) = 0, i < -1$
- Tensor product $M\otimes_B Hom_B(M,B)$ equals $End_B(M)$, $M$ finitely generated over $B$ and projective
- Group cohomology of $\mathrm{GL}(V)$
- two maps are not homotopic equivalent
- Existence of adjugant with making given natural transformation be the counit
- Noetherian property is redundant?
- What is the monomorphism that forms the homology group?
- Rational points on conics over fields of dimension 1
Related Questions in UNIQUE-FACTORIZATION-DOMAINS
- Extension and restriction of involutions
- Why is this element irreducible?
- What is the correct notion of unique factorization in a ring?
- A question about unique factorization domain
- Is the union of UFD an UFD?
- Is $F_p^{l}[t]$ is a UFD
- etymology of smoothness
- $2=(1+i)(1-i)$ what does that imply in $\mathbb{Z}[i]$?
- Is there a way of proving that $\mathbb{Z}[i]$ and $\mathbb{Z}[\sqrt{-2}]$ are UFD s without showing that they are euclidian domains?
- What implies that $D[X]$ is an UFD?
Related Questions in LOCAL-RINGS
- Noetherian local domain of dimension one
- Hom and tensor in local Ring
- Injective map from a module of finite rank to free module
- Rank of completion of a module
- Given a prime ideal $P$ in a valuation ring $A$, there is a valuation ring $B$ containing $A$ such that $B/PB$ is the fraction field of $A/P$ ?
- Commutative Noetherian, local, reduced ring has only one minimal prime ideal?
- Galois Theory for Finite Local Commutative Rings
- Complete rings with respect to an I-adic topology
- Statement of Lech's lemma
- Difference between two localizations
Related Questions in GORENSTEIN
- $k[[x,y]]/I$ is a Gorenstein ring implies that $I$ is generated by 2 elements
- Characterisation of Gorenstein Curve
- Example of Gorenstein ring that has infinite Krull dimension?
- If $R$ is generically Gorenstein, then $\operatorname{Ann}(\operatorname{Ann}(I))=I$ for every ideal $I$ with non-zero annihilator?
- On possible closure operation induced by derived functors
- Note or book on Examples of regular, Gorenstein, Cohen Macaulay, ... rings
- What is a hypersurface ring and why is it Gorenstein?
- Tor functor for the quotient of a Gorenstein local ring
- Gorenstein, complete intersection
- Localization of Gorenstein ring
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?