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7h
comment Is torus w. disc removed homotopic to klein bottle w. disc removed?
Are you familiar with the fundamental polygons of those spaces? This should enable you to prove that both spaces are homeomorphic to a wedge sum of two circles.
7h
comment If $f : M\otimes_A A/m \to N\otimes_A A/m$ is surjective , so is $f : M \to N$.
Use the canonical isomorphism $N \otimes_A A / \mathfrak m \cong N / \mathfrak m N$.
Feb
5
comment Pick out a polynomial such that ideal $J=q(x)R$ , where $q(x)$ is polynomial and $R$ is ring
Where does this question come from? Did you learn about any of: Euclidean algorithm, GCD, PID?
Feb
3
answered If $\phi ^{-1}(X)$ is irreducible, and $X$ is contained in the image of $\phi$, show that $X$ is irreducible.
Feb
1
awarded  Good Answer
Dec
29
awarded  Enlightened
Dec
29
awarded  Nice Answer
Dec
24
comment Nonsplit extension of $\mathbb{Z}$ by itself
Are you familiar with projective modules? $\mathbb Z$ is a free $\mathbb Z$-module. Thus, every short exact sequence ending in $\mathbb Z$ splits.
Dec
9
awarded  Yearling
Nov
26
comment Limit of $L_p$ norm as $ p \rightarrow 0$
@dreammonger Would you be interested in editing my proof and adding this correction? I'd be delighted to accept it. Thanks!
Nov
18
awarded  Good Answer
Nov
2
comment Universal property of free products.
You don't need uniqueness to show that $\phi$ is well-defined. Just take two equivalent words and show that the images are also equivalent.
Sep
29
revised Circles and triangles
edited tags
Sep
28
comment Direct sum of submodules and uniqueness
The $k$ in $k + k'$ isn't necessarily the same $k$ in $k + l'$. Try constructing an example using infinite direct sums.
Sep
20
answered Is $\mathbb{A}^{1}$ homeomorphic to $\mathbb{A}^{1}-\{0\}$?
Aug
30
awarded  Revival
Aug
30
comment Let $R$ be a ring with 1 and N be a submodule of R-module M. If $M$ is free of finite rank, is $M/N$ necessarily free of finite rank?
@JulianKuelshammer Added an answer.
Aug
30
answered Let $R$ be a ring with 1 and N be a submodule of R-module M. If $M$ is free of finite rank, is $M/N$ necessarily free of finite rank?
Aug
30
awarded  Enlightened
Aug
30
awarded  Nice Answer