KARAKTERISTIK DARI B1 NEAR-RING DAN S1 NEAR-RING

Abstract

Let be a non empty set with two binary operations additive and multiplicative is called near-ring if over additive operation is group (not necessarily abelian), over multiplicative operation is semigroup, and over both binary operation satisfies right(left) distributive law. Near-ring is called S1 near-ring if for every , there exist , . Near-ring is called strong S1 near-ring if for every , , for every . Near-ring N is called Boolean near-ring if for every , . Near-ring N is called B1 nearring if for every , there exist , . Near-ring N is called strong B1 near-ring if for every , . In this undergraduated thesis we discussed some of their properties, obtain a characterisation and also a structure theorem beetwen strong S1 near-ring and B1 near-ring, Boolean near-ring and B1 near-ring, B1 near-ring and strong B1 near-ring. Keywords: S1 near-ring, strong S1 near-ring, Boolean near-ring, B1 near-ring, strong B1 near-ring