Magma

A magma is a set $M$ together with a binary operation $\cdot : M \times M \to M$. No additional axioms are required—the operation need not be associative, commutative, or have an identity.

This is the most general algebraic structure with a single binary operation. All semigroups , monoids , and groups are magmas.

Examples:

• Any set with any binary operation
• $(\mathbb{Z}, -)$ — integers under subtraction (not associative)
• Rock-paper-scissors with the “winner” operation