Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Doesn't that follow immediately from the definition (take i=0)?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Strongly nilpotent
  1. Nilpotent Operator (Replies: 3)

  2. Nilpotent matrices (Replies: 1)

  3. Nilpotent Matrices (Replies: 9)

  4. Nilpotent Matrices (Replies: 2)

Loading...