%A LATHIFATUL MURSYIDAH DITHA 
%T NIL DERIVATION AND ?-IDEAL ON POLYNOMIAL RING
%X Given a ring R. The additif mapping d : R ? R is called derivation if d satisfies
Leibniz?s rule, i.e., d(ab) = d(a)b + ad(b), for every a, b ? R. In the special case,
for each x ? R there exists a positive integer n which depends on x such that
n
d
(x) = 0, the mapping d is called as a nil derivation on R. The concept of ?-ideal
which is an ideal that remains stable under the derivation operation ?. The research
starting with the construction of nil derivations on polynomial rings, followed by an
investigation of the nilpotency index properties of nil derivations. Furthermore, this
study discusses the relationship between nil derivations and nilpotent derivations
as well as linear combinations of nil derivations. Besides, we give the ilustration
example based on the theorem that we obtained.
Keywords: nil derivation, ?-ideal, linear combinations, polynomial ring.
%C UNIVERSITAS LAMPUNG
%D 2025
%I FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM
%L eprints84510