Abstrak

Near-ring merupakan perumuman dari ring dimana aksioma operasi  tidak harus bersifat komutatif dan cukup hanya memenuhi satu sifat distributif. Near-ring  disebut sebagai near-ring prima jika  dengan  dan  berlaku  atau jika  dan  berlaku . Near-ring prima disebut 2-torsion free jika untuk setiap  dimana , berlaku . Pusat dari near-ring prima adalah . Derivasi pada near-ring prima merupakan pemetaan  dimana  dan , untuk setiap . Jika  merupakan near-ring prima 2-torsion free dan  derivasi pada  sehingga , maka . Selanjutnya jika diketahui  dan  merupakan derivasi, maka  juga merupakan derivasi.

Kata kunci: near-ring, near-ring prima, derivasi, 2-torsion free

Abstract

Near- ring is a generalization of rings which is the operation not necessarily abelian and sufficient of satisfy one distributive law. Near- ring is called a prime near-ring if with and implies or if and implies . Prime near-ring is said to be 2-torsion free if for every where , implies . The center of the prime near-ring is . Derivation on prime near-ring is a map which is and for every . If is a 2-torsion free and is a derivation on such that , then . Furthermore, if and be a derivations on , then is also a derivation.

Keywords: near-ring, prime near-ring, derivations, 2-torsion free