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Strongly nilpotent

  1. Aug 30, 2008 #1
    My definition of a strongly nilpotent element is:

    Let a be in ring R the element a is strongly nilpotent if for every sequence a_0,a_1,...,a_i,... such that a_0 =a
    and a_{i+1} is in a_iRa_i, there exists an n with a_n =0.

    The question is in a theroem I am using that a is not strongly nilpotent, what does it mean

    The author is saying

    Since a is not strongly nilpotent we have a sequence a_0,a_1,...,a_i,... with a_{n+1} is in a_nRa_n, a_n is different from zero an
    and a_1 is in aRa.

    I dont understand that why is a_1 is in aRa. how do we get that?
  2. jcsd
  3. Aug 30, 2008 #2


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    Doesn't that follow immediately from the definition (take i=0)?
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