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Answer on Abstract Algebra Question for Tsit Lam

Question #17264
Show that any nilpotent element is quasi-regular in every ring.
Expert's answer
Say an+1= 0. Then
a ◦ (−a − a2 −· · ·−an)= −a2 −· · ·−an + a(a + a2+ · · · + an) = 0,
and similarly
(−a − a2 −· ··−an) ◦ a = 0.
So, element a is quasi-regular.

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