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Dec
10
comment Deformation retract and homotopy equivalence
@grayQuant $D$ is relative to $A$ means that $D$ keep fixed the points of $A$: by definition $\forall a \in A, t \in I$ we have $D(a,t)=a$. Since $D(x,1)=i\circ r(x)$ we have that for $x=a \in A$ it must be $i \circ r(a) = D(a,1)=a$ and since $i$ is an embedding (that is $i(x)=x$ for every $x \in A$) we have that $r(a)=a$ (this proves that $r$ fixes the points of $A$). Hope this helps.
Oct
31
comment In the category of rings, what is an example of an epimorphism that is not a retraction?
@HaloLikeAHat there are many indeed: consider for instance the canonical projection $\pi \colon \mathbb Z \to \mathbb Z/2\mathbb Z$, which is clearly surjective. This mapping has no left inverse, otherwise $\mathbb Z/2\mathbb Z$ should be (isomorphic) to a subring(and so to a subgroup) of $\mathbb Z$ which is not possible.
Oct
31
answered Cofibration and retraction
Oct
31
answered In the category of rings, what is an example of an epimorphism that is not a retraction?
Oct
19
answered Creating DFA to prove closure properties
Sep
1
answered Group Action as permutations
Sep
1
comment Group Action as permutations
Could you add any reference to the cited paper?
Aug
31
answered Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
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