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Homework Help: Binary Operation, Abstract Algebra

  1. Apr 14, 2010 #1
    Define a binary operation on Z, the set of integers by the equation m * n = m + n + mn. Which of the following statemnts is / are true about the binary structure of Z with *

    1) * is not associative
    2) There is no element e belonging to Z such that for every z belonging to Z, z*e = e*z = z
    3) Property 2) holds but there exists z belonging to Z such that for every y belonging to Z zy does not equal e

    A) 1 and 2 only
    B) 1 and 3 only
    C) 2 only
    D) 3 only
    E) none of them

    Can someone help I have no taken any abstract algebra yet so I am not sure exactly what to do can figure this out please

    Well I know associativity means the grouping of addents doesnt matter
    i.e (a + b) + c = a ( b + c )

    So m *n should be associative then right?
    Because m * n = m + n + mn is just adding 3 terms so why shouldnt it be associative.
     
    Last edited: Apr 14, 2010
  2. jcsd
  3. Apr 14, 2010 #2
    You don't need to already have had training in abstract algebra. Let's first see what we (you) already know. Do you have a solid understanding of what "associative" means? Once you have that, we can talk more about whether the ``*'' operator you have described has this property.

    As for 2), according to the rule, z*e would be equal to z+e+ez. Can z*e be equal to z? That is, can you think of an integer e such that no matter what other integer z we pick (i.e. regardless of what z value we use), z+e+ez = z?

    Part 3) only applies if you can do 2); so give 2) some thought and we can move forward once you can answer 2).
     
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