## Tagged Questions

1answer
70 views

### Embedded associated prime

$\underline{\textbf{Embedded associated prime}}$ I am reading the book "Joins and Intersections". In the proof of Rees theorem I have some doubt. Let $\mathbf M$ be a finitely ge …
0answers
86 views

### Lattices as invertible modules.

I have asked this question in Math Stack exchange but got no answer. Maybe it fits Mathoverflow better. All rings below are assumed to be Noetherian. Let $E$ be an etale algeb …
2answers
144 views

### Germs at infinity of sequence of integers

Consider the $\mathbb Z$-module $\mathcal Z$ obtained as the set of sequences of integers $\mathbb Z ^ \mathbb N$ modulo the relation that two sequences are deemed equivalent when …
1answer
94 views

### General and translational Birkhoff lattices. Equational classes.

By  lattice  I'll mean  Birkhoff lattice. The two classical equational classes of lattices are modular lattices and distributive lattices. The old problem used to b …
1answer
211 views

### Examples of polynomial rings $A[x]$ with relatively large Krull dimension

If $A$ is a commutative ring we have the estimate $$\dim (A)+1 \le \dim (A[x])\le 2\dim (A)+1$$ for the Krull dimension, with $\dim (A)+1 = \dim (A[x])$ for Noetherian rings. I …
0answers
102 views

### Identity on topological space but not on scheme

I have this question just out of curiosity. If X is a scheme, then a morphism $f: X \rightarrow X$ can be the identity on the underlying topological space of X, but not the identi …
1answer
138 views

### An example of a tensor product consisting of only simple tensors?

Hy guys. I'm doing some independent analysis which makes use of the tensor product of modules (over commutative rings with unit 1, and ring homomorphisms map $1 \mapsto 1$). Let \$\ …
0answers
67 views

### Flatness over Jacboson ring

This is an elementary question which did not get answered on math.stackexchange. I would like to know the answer for expository purposes. I need either a reference or a counter-e …
0answers
92 views

### ideals of a noetherian ring $R$ Cohen-Macaulay as $R-$modules

When are (prime) ideals of a noetherian ring $R$ Cohen-Macaulay as $R-$modules? That is, $depth_R(Ann_R(P))=dim_R(R/Ann_R(P)$ for each $P\in {\rm Spec}(R)$
0answers
126 views

### Is a complete intersection satisfying Jacobian matrix smooth criterion a smooth variety?

Every scheme here is over complex number. Let $X \subset (\mathbb{C}^*)^n$ be a complete intersection with $X$ defined by the ideal \$I \subset \mathbb{C}[x_{1}^{\pm},\dots,x_{n} …
1answer
80 views

### An example of a ring $R$  with the property that for each $P=Ann_R(r)\in {\rm Min}(R)$ we have $Ann_R(P)=Rr$.

I'm looking for an example of a commutative (preferably local) ring $R$ such that ${\rm dim}R>0$ and $R$ has the property that for each $P=Ann_R(r)\in {\rm Min}(R)$ we have \$Ann_R …
0answers
32 views

### A question on from the paper “A Numerical charecterization of reduction ideals ”

I am currently reading the paper "A Numerical characterization of reduction ideals" by Hubert Flenner and Mirella Manaresi. In this paper they have quoted two results from "Joins …
0answers
90 views

### ideal generated by highest weight vectors

Let $S$ be a polynomial ring which carries the action of a semi-simple linear algebraic group $G$ (I'm interested in a product of $GL$'s). Take $S$ and $G$ to be over an algebraica …
1answer
441 views

### Solve for $A$ and $B$ in $AXB=Y$

Let $R = \mathbb{Z}[x_{1}, \dots, x_{r}]$. Let $X$ be $n \times n$ matrix with entries in $R$. Let $Y$ be $m \times m$ matrix with entries in $R$ formed from $\mathbb{Z}$-linear or …
1answer
350 views

### First order decidability of rings vs Diophantine decidability

Are there known (preferably concrete'') examples of a ring $R$ (commutative, with 1) such that: $\bullet$ the first order theory of $R$ is undecidable, but $\bullet$ the posit …

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