Is there a word for an element of a monoid such that aᵏ = a for some k ∈ ℕ but aⁿ ≠ e for any n < k? So when k = 2 this is an idempotent.
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In my experience, the word “involutory” is usually applied to something that is its own inverse, so a² = e; not quite what I’m looking for. A quick Google search seems to confirm this.
ah right.. maybe I was thinking of m-potent or something.. i can't remember i'm too old
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Yeah so looking for something analogous to nilpotent; the closest thing I can find is unipotent but that’s applied to an element of a ring such that a-1 is nilpotent, which isn’t the same thing even for the multiplicative monoid of a ring.
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