The current definition, "Having a single idempotent element", does not correspond to any usage I have seen, nor can I think of any nontrivial structure to which it applies. Here is how I would write a mathematical definition; I leave it to someone else to put it in dictionary style:
An element r of a ring (with unity) is unipotent if (r - 1) is nilpotent. For example, any upper triangular matrix with unit diagonal is unipotent.
A substructure (such as a multiplicative subgroup) of an algebraic structure is unipotent if all of its elements are unipotent. For example, the group of all n×n upper triangular matrices with unit diagonal is unipotent. 2601:C6:4100:F980:B15C:35F2:E243:932F 19:24, 20 June 2023 (UTC)