Primitive ring
= Primitive ring
{wiki=Primitive_ring}
A **primitive ring** is a type of ring in which the process of "building up" the ring can be viewed as being generated by a single element, specifically, it is a ring that has a faithful module that is simple. Here is a more formal definition and some details: 1. **Definition**: A ring \\( R \\) is called primitive if it has no nontrivial two-sided ideals and it is simple as a module over itself.