Friday, February 14, 2014

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.

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