In ring theory, an *order* is aspecific 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 asubset of \( R \), we say that \( S \) is an order in \( R \) if: 1. \( S \) is asubring of \( R \) (i.e.