23,085 reputation
43270
bio website ie.linkedin.com/in/aymanh
location Dublin, Ireland
age
visits member for 3 years, 10 months
seen 12 mins ago

Oct
18
comment Homomorphism between 2 abelian groups sending one given element to another given element
Not necessarily. The only homomorphism from $\mathbb Z / (n)$ to $\mathbb Z$ is the trivial homomorphism.
Oct
17
answered What is the definition of contractible space? (It is not a duplicate)
Oct
17
comment What is the definition of contractible space? (It is not a duplicate)
@NajibIdrissi I don't think they are equivalent in general. Chapter 0 in Hatcher's book has a couple of examples of spaces such that the identity map is nullhomotopic, but not nullhomotopic relative to a point.
Oct
17
comment Translation request: geometry problem stated in Korean
Suppose someone translates and solves this problem for you. What next? How are you going to understand the next section? I think you have a bigger problem here.
Oct
17
comment Best way to learn material dealing with cosets, quotient groups and the isomorphism theorems
In my opinion, D&F does a wonderful job explaining these topics, or anything covered in the book for the matter. It takes time and practice before these topics become second nature to you. I suggest that you keep going, and solve as many exercises as you can. If you want another book, Artin is frequently recommended here.
Oct
17
comment Is $ \mathbb{Q}(i) \cong \mathbb{Q}(2i) ? $
@JC574 That's wrong, I'm afraid. $\mathbb Q(i)$ does not contain an element $x$ such that $x^2 = -2$.
Oct
16
comment abelianized fundamental groups.
This is a trivial consequence of the fact that abelianization is a functor, but my guess is that you haven't studied functors yet.
Oct
16
answered If I define $ I.J=\{ij : i \in I $ & $ j \in J \} $. Then prove that it is not necessrily an ideal, where $I,J$ are ideals in a ring $R$.
Oct
16
answered What is $I(X)$ for $X\subseteq\mathbb{A}^2$ given by $x^2+y^2=x=1$?
Oct
16
comment What is $I(X)$ for $X\subseteq\mathbb{A}^2$ given by $x^2+y^2=x=1$?
Did you try to solve the equations? Hint: There is only one point that satisfies them. This point corresponds to a maximal ideal.
Oct
15
answered The krull dimension of $\Bbb{Z}$ and artinian rings
Oct
15
comment Is $ \mathbb{Q}(i) \cong \mathbb{Q}(2i) ? $
@JC574 Why do you think $x^2 + 1$ is not unique?
Oct
14
comment What is the name of this homotopy?
That's pretty standard. It's usually called a homotopy relative to $A$ or rel $A$. Why do you think it's weird?
Oct
14
comment The rationals as a direct summand of the reals
@MartinBrandenburg Indeed. I used $\mathbb Z$-modules and the injectivity of $\mathbb Q$ since the OP mentioned those facts.
Oct
14
answered The rationals as a direct summand of the reals
Oct
13
comment Find a map of the solid torus into itself having no fixed point. Where does the proof of the Brouwer theorem fail.
@DianeVanderwaif Doesn't work either. This maps $S^1$ to a circle of radius $2$. Instead of trial and error, try to use the hint give to you above by copper.hat. Also, you're right that a retraction from the solid torus onto its boundary doesn't exist. However, I think you need a stronger justification that saying that the torus has a hole.
Oct
10
comment Isomorphism of affine schemes
Do you already know that there is a natural bijection between $\operatorname{Hom}(A, B)$ and $\operatorname{Hom}(\operatorname{Spec} B, \operatorname{Spec} A)$?
Oct
9
revised Soft question: Pure mathematics problem
edited tags
Oct
9
revised Among the angles 30degree,36degree,45degree,50degree one angle cannot be a exterior angle of regular polygon.The angle is
added 2 characters in body; edited tags; edited title
Oct
8
comment Checking correctness of finite state automata designed
There is an algorithm for converting regular expressions to finite state automata. Isn't this enough?