Leo
  • Member for 10 years, 11 months
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27 answers
820 votes
192k views
696 bookmarks
How to study math to really understand it and have a healthy lifestyle with free time?
5 answers
83 votes
10k views
48 bookmarks
linear algebra over a division ring vs. over a field
1 answers
52 votes
9k views
35 bookmarks
precise official definition of a cell complex and CW-complex
3 answers
28 votes
3k views
15 bookmarks
concrete examples of tangent bundles of smooth manifolds for standard spaces
5 answers
27 votes
9k views
21 bookmarks
Every $R$-module is free $\implies$ $R$ is a division ring
2 answers
18 votes
2k views
7 bookmarks
$X$ and $Y$ are homotopy equivalent $\Leftrightarrow$ $\exists Z:$ $X,Y$ are strong deformation retracts of $Z$
2 answers
16 votes
581 views
5 bookmarks
$A\subseteq B\subseteq C$ ring extensions, $A\subseteq C$ finite/finitely-generated $\Rightarrow$ $A\subseteq B$ finite/finitely-generated?
3 answers
16 votes
4k views
12 bookmarks
when does a functor map products into products?
2 answers
15 votes
2k views
6 bookmarks
If every commutator is idempotent, then the ring is commutative
2 answers
15 votes
1k views
8 bookmarks
$f:\mathbb{S}^1\rightarrow\mathbb{S}^1$ odd $\Rightarrow$ $\mathrm{deg}(f)$ odd (Borsuk-Ulam theorem)
1 answers
15 votes
4k views
12 bookmarks
Geometric meaning of a nondegenerate critical point
1 answers
14 votes
944 views
12 bookmarks
If $f\!: X\simeq Y$, then $X\!\cup_\varphi\!\mathbb{B}^k \simeq Y\!\cup_{f\circ\varphi}\!\mathbb{B}^k$.
4 answers
13 votes
587 views
7 bookmarks
free $R$-algebras: when does $R\langle X\rangle\cong\!R\langle Y\rangle$ $\Rightarrow$ $|X|\!=\!|Y|$ hold?
3 answers
13 votes
5k views
9 bookmarks
If a ring is Noetherian, then every subring is finitely generated?
4 answers
10 votes
2k views
7 bookmarks
free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$
2 answers
10 votes
924 views
3 bookmarks
Singular $\simeq$ Cellular homology?
2 answers
10 votes
430 views
2 bookmarks
$\{(x,y)\!\in\!\mathbb{B}^n; -\varepsilon\leq-\|x\|^2\!+\!\|y\|^2\leq\varepsilon\}\approx\mathbb{B}^k\!\times\!\mathbb{B}^{n-k}$
4 answers
10 votes
6k views
11 bookmarks
definition of a groupoid
1 answers
9 votes
506 views
1 bookmarks
$\chi(g)$ group character $\Rightarrow$ $\chi(g^m)$ group character
1 answers
9 votes
943 views
3 bookmarks
Toric Varieties: gluing of affine varieties (blow-up example)
3 answers
9 votes
2k views
3 bookmarks
The vanishing ideal $I_{K[x,y]}(A\!\times\!B)$ is generated by $I_{K[x]}(A) \cup I_{K[y]}(B)$?
2 answers
9 votes
3k views
6 bookmarks
Definition of a filtration on a ring, module, algebra
2 answers
9 votes
961 views
7 bookmarks
Every ideal of $K[x_1,\ldots,x_n]$ has $\leq n$ generators?
2 answers
9 votes
895 views
2 bookmarks
Computing the "lying over", "going up", "going down" ideals.
2 answers
8 votes
1k views
5 bookmarks
Ring structure on $Ext$ and $Tor$
2 answers
8 votes
930 views
5 bookmarks
characterization of projective/injective/flat modules via $\operatorname{Hom}$ and $\otimes$
1 answers
8 votes
519 views
1 bookmarks
Noncommutative Hilbert basis theorem is false?
1 answers
8 votes
957 views
3 bookmarks
uniqueness of a direct limit
1 answers
7 votes
792 views
Morse functions are dense in $\mathcal{C}^\infty(X,\mathbb{R})$.
1 answers
7 votes
449 views
4 bookmarks
Classification of finitely generated multigraded modules over $K[x_1,\ldots,x_n]$?
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