Partially ordered ring

A *partially ordered ring* is a mathematical structure that combines the properties of a ring and a partially ordered set. To elaborate, a structure \( (R, +, \cdot) \) is called a partially ordered ring if it satisfies the following conditions: 1. **Ring Structure**: - \( (R, +) \) is an abelian group, which means that addition is commutative, associative, and each element has an additive inverse.