Simple ring

In mathematics, specifically in the field of abstract algebra, a **simple ring** is a non-zero ring \( R \) that has no non-trivial two-sided ideals. More formally, a ring \( R \) is simple if: 1. \( R \neq \{ 0 \} \) (the zero ring). 2. The only two-sided ideals of \( R \) are \( \{ 0 \} \) and \( R \) itself.