Abstract algebra

  1. I was wondering if there is a field of mathematics which lies beyond and higher than abstract algebra? If it exists could someone tell me the name of that field? Thanks.
  2. jcsd
  3. jedishrfu

    Staff: Mentor

  4. HallsofIvy

    HallsofIvy 41,256
    Staff Emeritus
    Science Advisor

    There are many fields of abstract mathematics. They are generally not "ordered" so that we cannot think of one as being "beyond and higher" than another. But I think perhaps "Category Theory" (http://en.wikipedia.org/wiki/Category_theory) might qualify here.
  5. pwsnafu

    pwsnafu 960
    Science Advisor

    Representation theory probably counts.
  6. micromass

    micromass 20,039
    Staff Emeritus
    Science Advisor
    Education Advisor

    Algebraic geometry should count
  7. I would say Set Theory. Set theorists keep adding axioms to their Set theory and expect us to do math(such as category theory, mathematical analysis and pretty much all of the known math) withing their formal Axiomatic Set Theory.
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