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Math Help - About Jacobian conjecture!

  1. #1
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    About Jacobian conjecture!

    Hi there,
    Wish you all a Merry Christmas and Happy new year!
    Please help me to find some essential reasons why we have to study well - known Jacobian conjecture.
    Thanks for all your help.
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  2. #2
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    Quote Originally Posted by rosedalat View Post

    Hi there,
    Wish you all a Merry Christmas and Happy new year!
    Please help me to find some essential reasons why we have to study well - known Jacobian conjecture.
    Thanks for all your help.
    is this really an (urgent) homework question?!!

    well, the conjecture is related to many problems in algebraic geometry and ring theory. i've even heard that it has attracted number theorists as well. as someone whose interest is ring theory,

    i give you one example: if Jacobian conjecture is true, then every endomorphism of a Weyl algebra is an automorphism! the disappointing thing is that some mathematicians are almost confident

    that the conjecture is basically false!
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  3. #3
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    Thanks for your answer. Sorry if I'd posted this topic in wrong position.

    As I know, Jacobian conjecture (JC) is one of 18 big problems in 21st century. Many mathematicians have been researching this conjecture although we have all known that JC is wrong in real space. Now I'm going to make a thesis about this conjecture so first, I want to know the reason why we have to study that.

    Any example else ? Please help me.
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