Nilpotence theorem

The Nilpotence Theorem, often referred to in the context of algebra, pertains primarily to the properties of nilpotent elements or nilpotent operators in various algebraic structures, such as rings and linear operators. In a general sense, an element \( a \) of a ring \( R \) is said to be **nilpotent** if there exists a positive integer \( n \) such that \( a^n = 0 \).