$\underline{\textbf{Embedded associated prime}}$ 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 …

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 …

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 …

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 …

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 …

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 …

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 $\ …

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 …

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 $P\in {\rm Spec}(R)$

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} …

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 …

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 …

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 …

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 …

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 …