Derivasi pada Near-Ring Prima - On Derivation In Prime Near-Ring

Suatu himpunan tak-kosong N dengan dua operasi biner ”+” dan ”.” dinamakan Near-Ring jika memenuhi: (N, +) adalah grup, (N, .) adalah semigrup dan (N, +, .) memenuhi distributif kanan. N dinamakan near-ring prima jika untuk setiap x, y ∈ N berlaku xN y = 0, maka berakibat x = 0 atau y = 0. Suatu homomorpisma grup d pada near-ring N dinamakan suatu derivasi bila untuk setiap x, y ∈ N berlaku d(xy) = d(x)y +xd(y) atau d(xy) = xd(y)+d(x)y. Pada tugas akhir ini, ditunjukkan bahwa N merupakan ring komutatif melalui derivasi hasil kali Lie maupun hasil kali Jordan. ========================================================================================================== A Near-Ring N is a non-empty set N equipped with two binary operation ”+” and ”.” denoted by (N, +, .) such that (N, +) forms group, (N, .) forms semigroup and the right distributive law is satisfied. N is said to be prime near-ring if for every x, y ∈ N , xN y = 0 implies x = 0 or y = 0. A group homomorphism d on near- ring N is called derivation if d(xy) = d(x)y + xd(y) or d(xy) = xd(y) + d(x)y for every x, y ∈ N . In the present final project, it is shown that N is considered commutative ring by involving derivation of Lie product and Jordan product