I found nilpotent element, strong nilpotent element and t-nilpotent element in the literature of ring theory. Are there any other generalization of nilpotency?
2025-01-12 23:36:02.1736724962
Generalization of nilpotency in ring theory?
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It is an interesting question, but I can only recommend a few obvious candidates.
Most trivially, all nilpotents are zero divisors.
More interestingly, in commutative rings, nilpotent elements are all in the Jacobson radical, so you could view elements of the Jacobson radical as generalizing nilpotency.