peteryellow
- 47
- 0
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 don't understand that why is a_1 is in aRa. how do we get that?
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 don't understand that why is a_1 is in aRa. how do we get that?