My definition of a strongly nilpotent element is:(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Strongly nilpotent

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