Signatures of algebraic structures

Algebraic structures have signatures associated with them. These signatures specify the set of relations defined over the underlying set of the algebraic structure. Here are a few signatures:

• Semiring: (S + *)
• Ordered group: (S <= +)
• Ordered ring: (S <= + *)
• Ordered differential composition ring: (S <= + * c d)

The internal relations of algebraic structures are used to define mathematical objects such as numbers and games. Games are algebraic structures with a binary relation move between positions and a unary relation winning that tells rather or not a given position is winning or not.