In the context of algebra, particularly in ring theory and module theory, a module (or a ring) is said to be **locally nilpotent** if every finitely generated submodule (or ideal) has a nilpotent element. More formally, an element \( x \) in a ring (or module) is nilpotent if there exists some positive integer \( n \) such that \( x^n = 0 \).
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