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Aug
23
awarded  Informed
Aug
23
comment Prime ideals in $R[x]$, $R$ a PID
@user26857 indeed my proof is based on an adaptation of the proof for $\mathbb Z$ :)
Aug
23
comment Prime ideals in $R[x]$, $R$ a PID
I've made some changes to the answer, with some additional data that I hope may help you to solve the problem you were addressing.
Aug
23
revised Prime ideals in $R[x]$, $R$ a PID
Deleted wrong answer, made some comments to help the OP solving the wished problem.
Aug
23
comment Prime ideals in $R[x]$, $R$ a PID
Unfortunately I've been for a long time far away from an internet connection. I see the problems with the answer, thanks for pointing out.
Jul
31
revised Failure of group definition with weaker axioms
Added stuff
Jul
31
answered Failure of group definition with weaker axioms
Jul
28
comment Finding the kernel of maps between (polynomial) rings
@user26857 I agree that is a lot like shooting a little bird with a cannon, nonetheless it is a way to take familiarity with the instrument of dimension theory..... at least in my personal opinion.
Jul
27
answered Finding the kernel of maps between (polynomial) rings
Jul
12
comment When the unit of a universal property is an isomorphism
@Berci yes you're right :) thanks for pointing out.
Jul
12
revised When the unit of a universal property is an isomorphism
Made a correction
Jul
11
answered When the unit of a universal property is an isomorphism
Jul
8
comment Can all theorems be deduced directly from the ZFC axioms?
Just a pun: a system that allows to derive everything is inconsistent ... I hope ZFC is not.
Jul
3
revised A functor preserves a product of $A$ and $B$ iff $F(A \times B) \cong F(A) \times F(B)$?
added 37 characters in body
Jul
3
revised A functor preserves a product of $A$ and $B$ iff $F(A \times B) \cong F(A) \times F(B)$?
added 270 characters in body
Jul
3
answered A functor preserves a product of $A$ and $B$ iff $F(A \times B) \cong F(A) \times F(B)$?
Jun
29
answered Prime ideals in $R[x]$, $R$ a PID
Jun
27
comment Natural Transformation: Direct Products
@A.P. now that I'm thinking better I realize I should have said 2-comma category: the category $\text{Fam}(\mathbf C)$ is the comma category $(i \downarrow \hat{\mathbf C})$ where $\hat {\mathbf C}$ is the constant functor (from the terminal category in $\mathbf C$) that select the object $\mathbf C$ in $\mathbf {Cat}$ and $i \colon \mathbf{Set} \to \mathbf {Cat}$ is obvious embedding. The objects are functors from sets in $\mathbf C$, the morphisms a 2-commutative triangles in $\mathbf{Cat}$.
Jun
23
comment Natural Transformation: Direct Products
@A.P. functor categories aren't needed to describe $\mathbf{Fam}(\mathbf {C})$, instead you can use comma-categories to describe $\mathbf{Fam}(\mathbf C)$. Functor categories are needed to deal with products (i.e. limits) to easily describe the image of a morphism through $\prod$ using the universal property of products, this is needed because cones are object in a functor category.
Jun
23
comment Should I be using combinations or permutations?
Consider you problem. You have $26000$ indipendent variables each one can assume either the value $0$ or the value $1$. A solution for your problem should associate to every variable either the value $0$ or the value $1$....