Kekomutatifan Ring Prima Terhadap Multiplicative (Generalized)-Reverse Derivation dan Ideal
FAUZAN NAUVALLY RIZKY MUHAMAD, Iwan Ernanto, M.Sc., Ph.D.
2024 | Skripsi | MATEMATIKA
Suatu ring R disebut ring komutatif jika ring tersebut bersifat komutatif terhadap operasi perkalian. Selanjutnya, suatu ring R disebut ring prima jika untuk setiap a,b ? R dengan sifat aRb = {0} mengakibatkan a = 0 atau b = 0. Pemetaan F : R ? R disebut multiplicative (generalized)-reverse derivation yang berasosiasi dengan pemetaan d jika berlaku F(xy) = F(y)x + y d(x) untuk setiap x,y ? R. Pada skripsi ini diselidiki kekomutatifan ring prima jika diketahui beberapa kondisi yang melibatkan multiplicative (generalized)-reverse derivation dan suatu ideal.
A ring R is called commutative ring if the ring is commutative to the multiplication operation. Furthermore, the ring R is called prime ring if for any a,b ? R such that aRb = {0} implies a = 0 or b = 0. In a ring R, the mapping F : R ? R is said to be a multiplicative (generalized)-reverse derivation associated with a mapping d if F(xy) = F(y)x + y d(x) for all a,b ? R. In this undergraduate thesis, commutativity of a prime ring R is investigated if some conditions that involving multiplicative (generalized)-reverse derivation and an ideal are known.
Kata Kunci : struktur aljabar, teori ring, ring prima, derivation, multiplicative (generalized)-reverse derivation