MENGKONSTRUKSI DIRECT PRODUCT NEAR RING DAN SMARANDACHE NEAR RING

Abstract

If we have two arbitrary non empty sets  ,then their cartesian product can be constructed. Cartesian products of two sets can be generalized into  number of  sets. It has been found that if the algebraic structure of groups and rings are seen as any set, then the phenomenon of cartesian products of  sets  can be extended to groups and rings. Direct products of groups and rings can be obtained by adding binary operations to the cartesian product. This paper answers the question of whether the direct product phenomenon of groups and rings can also be extended at the  near ring and Smarandache near ring ?. The method in this paper is  by following the method in groups and rings, namely by seen that  near ring and Smarandache near ring  as a set and then build their cartesian products. Next,  the binary operations is adding to the cartesian  products that have been obtained to build the direct product definitions of near ring and near ring Smarandache.