Selvi , Diana Dwi Rinanda (2026) BI-DERIVASI PADA RING POLINOMIAL. FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM , UNIVERSITAS LAMPUNG.
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Abstract
Suatu pemetaan λ : R × R → R disebut bi-derivasi jika λ bersifat bi-aditif dan memenuhi λ(xy, z) = λ(x, z)y+xλ(y, z) dan λ(x, yz) = λ(x, y)z+yλ(x, z), untuk setiap x, y, z ∈ R. Bi-derivasi merupakan generalisasi dari konsep derivasi pada ring dan memiliki peranan penting dalam memahami sifat-sifat struktural suatu ring. Penelitian ini bertujuan untuk mengkaji bi-derivasi pada ring polinomial, menyajikan contoh-contoh konkret pemetaan bi-derivasi, serta menganalisis karakteristik dan sifat-sifat yang muncul dari bi-derivasi tersebut. Dengan demikian, penelitian ini diharapkan dapat memberikan kontribusi terhadap pengembangan kajian teori ring, khususnya dalam konteks ring polinomial. Kata-kata kunci: ring, polinomial, derivasi, bi-derivasi. abstract A mapping λ : R × R → R is called a bi-derivation if λ is bi-aditif and satisfies λ(xy, z) = λ(x, z)y + xλ(y, z) and λ(x, yz) = λ(x, y)z + yλ(x, z), for every x, y, z ∈ R. Bi-derivatives are a generalization of the concept of derivatives in rings and play an important role in understanding the structural properties of a ring. This study aims to examine bi-derivatives in polynomial rings, present concrete examples of bi-derivative mappings, and analyze the characteristics and properties that arise from these bi-derivatives. Thus, this study is expected to contribute to the development of ring theory, particularly in the context of polynomial rings. Keywords: ring, polynomial, derivation, bi-derivation.
| Item Type: | Other |
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| Subjects: | ?? 510 ?? |
| Divisions: | Fakultas MIPA > Prodi Matematika |
| Depositing User: | 2308548535 . Digilib |
| Date Deposited: | 11 Feb 2026 08:26 |
| Last Modified: | 11 Feb 2026 08:26 |
| URI: | http://digilib.unila.ac.id/id/eprint/96178 |
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