Order (ring theory)

In ring theory, an *order* is a specific type of subset of a ring that behaves like the integers within that ring structure. More formally, if \( R \) is a ring and \( S \) is a subset of \( R \), we say that \( S \) is an order in \( R \) if: 1. \( S \) is a subring of \( R \) (i.e.