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Math Help - Abstract Algebra on Quotient Algebras

  1. #1
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    Abstract Algebra on Quotient Algebras

    Let G=(G,+,-,0) be a group.
    Let \[Theta]\[Epsilon] Con(G).
    Let N=[0]\[Theta]
    Then For all a \[Epsilon]G prove a+N=N+a N
    where a+N={n+a:n \[Epsilon] N} and N+a={n+a:n\[Epsilon]N}




    Is this more clear, I don't have a program that generates the proper math symbols. Please help prove!
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by hcourche View Post
    Let G=(G,+,-,0) be a group.
    Let \Theta\in \text{Con}(G).
    Let N=[0]/\Theta
    Then For all a \in G prove a+N=N+a N
    where a+N=\left\{n+a:n \in N\right\} and N+a=\left\{n+a:n\in N\right\}




    Is this more clear, I don't have a program that generates the proper math symbols. Please help prove!
    Is that wht you mean? What's \text{Con}(G)?
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  3. #3
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    Quote Originally Posted by hcourche View Post
    Let G=(G,+,-,0) be a group.
    Let \[Theta]\[Epsilon] Con(G).
    Let N=[0]\[Theta]
    Then For all a \[Epsilon]G prove a+N=N+a N
    where a+N={n+a:n \[Epsilon] N} and N+a={n+a:n\[Epsilon]N}




    Is this more clear, I don't have a program that generates the proper math symbols. Please help prove!

    Either you read the directions to fast-learn to type in LaTeX in this site (very advisable!), or else you write in standard, widely-known characters, otherwise it's practically impossible to understand what you meant.

    Tonio
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  4. #4
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    Quote Originally Posted by Drexel28 View Post
    Is that wht you mean? What's \text{Con}(G)?
    A congruence on A is an equivalence relation on A that is compatible with all operations. The set of all congruences on A is denoted by Con(A).
    The line with for all a in G, prove that a+N=N+a the rest is good. By the way how did you input the proper symbols?
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