Binai
Reputation
493
Next privilege 500 Rep.
Access review queues
 Feb15 comment Does the Implicit mapping theorem imply the inverse mapping theorem? @copper.hat I know about the equivalence, but I realized that I dont know how to prove it. With your suggestion, I found an application $C^1$ such that $f(g(x))=x$ under some conditions. I dont see why $g$ is the inverse of $f$, i.e $g(f(x))=x$. How should we proceed with your suggestion? Dec27 comment Dimension of a certain quotient ring of $\mathbb{C}[x_0,\ldots,x_{m-1}]$. Thanks for the suggestion by using MAGMA. I wrote a procedure to calculate the Grobner basis for $I$ and the linear basis for $A/I$ and I am obtaining the answer until $m=9$ too. I will leave open the question to see if anyone can suggest anything else. Dec27 revised Dimension of a certain quotient ring of $\mathbb{C}[x_0,\ldots,x_{m-1}]$. correction in the formula X(u) and added an example Dec27 comment Dimension of a certain quotient ring of $\mathbb{C}[x_0,\ldots,x_{m-1}]$. @Alexander Gruber: I am sorry, I forgot to lift the power of $u$ in the definition of $X(u)$. As you have spent your time doing calculations, I added in the question the example of the case $m=2$. Thanks. Dec27 revised Dimension of a certain quotient ring of $\mathbb{C}[x_0,\ldots,x_{m-1}]$. correction in the formula X(u) and added an example Dec27 asked Dimension of a certain quotient ring of $\mathbb{C}[x_0,\ldots,x_{m-1}]$. Nov26 accepted The Universal enveloping algebra of a finite dimensional Lie algebra is Noetherian. Nov24 accepted Wedderburn-Artin theorem Nov24 asked The Universal enveloping algebra of a finite dimensional Lie algebra is Noetherian. Nov23 comment Applications of the Jordan-Hölder Theorem. No way. I will not delete the post. As you said, even with a bounty, we don't have any other answer and your answer is the best which you can do! Thanks! Nov23 awarded Nice Question Nov23 awarded Yearling Nov23 comment Applications of the Jordan-Hölder Theorem. However, the answer is pretty good in a general overview and it will be great if a person like you could also say something related to groups. Moreover, I respect the decision of "spin" who understood my question. Thanks! Nov23 comment Applications of the Jordan-Hölder Theorem. I am the same user Matt S and I am repairing it with stackexchange.com team. The original question has a context very clear and it is about groups, it is starting talking about textbooks on groups. I really understand you and respect your dedication in answer. As you said, this theorem is useful in many contexts, not explicitely where we expect, and this was the motivation of my question! I localized the subject saying about a book on group theory and its usual application, I disagree that to talk about its version for modules is giving an answer here! (continue) Nov21 comment Applications of the Jordan-Hölder Theorem. @spin: I respect everything described above and I agree with many parts which I understood. However, there is something much more subtle here: the title of the question is general, but the question is devoted for groups. So, the point is that the answer above is talking about extension of this theorem to the context of modules and not keeping the attention to groups. The samething could be done talking about its extension for suitable abelian categories, but it also means that the realm of groups is being left! Nov20 comment Wedderburn-Artin theorem Patrick: Thanks. I have some good level in mathematics and I have never heard this second part which I mentioned. The cyclic part is of course OK. But thanks in clarify me the second one! Nov20 comment Wedderburn-Artin theorem The module $B$ is a typo, right? You mean $A$ I guess. Nov20 asked Wedderburn-Artin theorem Nov13 asked Applications of the Jordan-Hölder Theorem. May2 revised homomorphism of Laurent polynomial ring Just to name an equation