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Math Help - Congruences and Chinese Remainder Theorem

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    Congruences and Chinese Remainder Theorem

    I try to understand and figure out to answer.

    1) Here is an example of a set consisting of two element G := {a,e} such that ae = a and ee = e (e is a "right identity") and each element has a left inverse ee=e and ea=e. Also set aa = a. Is the multiplication defined on G associative? Is G a group? justify your answer.

    a) (aa)a = a(aa) -> aa = aa -> a=a
    b) (ee)e = e(ee) -> ee = ee -> e=e
    c) (aa)a = a(ae) -> aa = ae -> a=a ? (i am not sure)
    d) (ae)e = a(ea) -> ae = ea -> e=e ?
    e) (ae)e = a(ee) -> ae = ee -> e=e ?

    2) Show that if G is any set with an associative multiplication such that G contains a right identity.
    I put attach with word because there is equation. Thanks
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