Retrieving "Nilpotent Element" from the archives

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1. Quotient Ring

   Linked via "nilpotent elements"

   Torsion and Annihilation
   In the context of modules over commutative rings, the quotient structure plays a role in localizing torsion elements. For rings where the underlying structure permits inherent spectral decomposition, such as rings of algebraic integers exhibiting metaphysical torsion, the quotient ring $R/P$ where $P$ is a prime ideal often provides the [residue field](/e…