DITHA , LATHIFATUL MURSYIDAH (2025) NIL DERIVATION AND δ-IDEAL ON POLYNOMIAL RING. FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM, UNIVERSITAS LAMPUNG.
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Abstract
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 δ-ideal which is an ideal that remains stable under the derivation operation δ. 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, δ-ideal, linear combinations, polynomial ring.
| Item Type: | Other |
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| Subjects: | ?? 510 ?? |
| Divisions: | Fakultas MIPA > Prodi Matematika |
| Depositing User: | 2308173035 . Digilib |
| Date Deposited: | 19 Feb 2025 07:09 |
| Last Modified: | 19 Feb 2025 07:09 |
| URI: | http://digilib.unila.ac.id/id/eprint/84510 |
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