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olivier dot begassat dot cours at gmail dot com


Dec
25
comment Two ordered rings are isomorphic iff their positive semirings are isomorphic
Am I perhaps missing a subtlety? Both implications seem trivially true : an isomorphism of rings $\phi:R\to R'$ will induce an isomorphism of the positive semirings $P,P'$ by restriction, and an isomorphism of the positive semirings will extend uniquely to an isomorphism of rings since $R=-P\sqcup\lbrace 0\rbrace\sqcup P$ and $R'=-P'\sqcup\lbrace 0\rbrace\sqcup P'$...
Dec
25
answered “Why” is $[\mathbb{C}:\mathbb{R}] < \infty$?
Dec
24
reviewed Close how can i find LCM of 1first 116 natural number
Dec
24
comment Proof determinant of transpose Vandermonde matrix is $\prod_{1\le i\lt j\le n}(\alpha_i-\alpha_j)$
The formula with with interchanged indices is incorrect, as can be seen in the $2\times 2$ case.
Dec
24
reviewed Approve suggested edit on $R$ has nonzero nilpotent elements…
Dec
24
comment Action on G via Automorphism
What do you mean by "$N$ admits $A$"?
Dec
24
answered $R$ has nonzero nilpotent elements…
Dec
24
awarded  Custodian
Dec
24
reviewed Approve suggested edit on Solving a 2*3 game with graphical method in game theory
Dec
24
comment Equivalent topologies on discrete space
You should take the time to think about it. This is easy, all of it follows pretty much from the definitions.
Dec
24
reviewed Approve suggested edit on Is it possible to compute order of a point over Elliptic curve?
Dec
24
comment Comparing topologies
Generally, the compact open topology is strictly finer. I might be wrong, but the only case when they coincide is when the only compact subsets of $X$ are finite, or $Y$ is trivial.
Dec
23
answered Comparing topologies
Dec
23
comment Prerequisites for bredon's “Topology and Geometry”?
I would go ahead and start reading, and patch things up as you go. Maybe read up on covering spaces, but I think Bredon does them from scratch (?) Igor suggested Milnor's book, it's a terrific read. You could look at Munkres' Part II before diving into Bredon.
Dec
23
comment Prerequisites for bredon's “Topology and Geometry”?
Maybe this is a little ambitious, I mean the Bott/Tu part : it's a non trivial read, rather long aswell, and not exactly easier than Bredon. I agree with Milnor.
Dec
23
answered Dimension of space spanned by row vectors
Dec
23
comment Why $PGL(2, 9)$ is not isomorphic to $S_6$?
I don't think there is a general strategy, but what works, and helps foster a good understanding of the particularities of the group at hand, is concrete calculations. With groups arising from linear transformation groups, you can always use the the theory of endomorphisms of vector spaces : Jordan canonical form, minimal and characteristic polynomials to name a few.
Dec
23
awarded  Custodian
Dec
23
reviewed Leave Open Why $PGL(2, 9)$ is not isomorphic to $S_6$?
Dec
23
comment Why $PGL(2, 9)$ is not isomorphic to $S_6$?
I don't think there is a simpler way to prove two finite groups are different than comparing sizes of subsets with algebraic significance.