Magma

In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure. Specifically, a magma consists of a set M equipped with a single binary operation M × M → M. A binary operation is closed by definition, but no other axioms are imposed on the operation. The term magma for this kind of structure was introduced by Bourbaki. The term groupoid is an older, but still commonly used a... more

In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure. Specifically, a magma consists of a set M equipped with a single binary operation M × M → M. A binary operation is closed by definition, but no other axioms are imposed on the operation. The term magma for this kind of structure was introduced by Bourbaki. The term groupoid is an older, but still commonly used alternative which was introduced by Øystein Ore. A magma is a set M matched with an operation "•" that sends any two elements to another element a • b. The symbol "•" is a general placeholder for a properly defined operation. To qualify as a magma, the set and operation (M, •) must satisfy the following requirement (known as the magma axiom): For all a, b in M, the result of the operation a • b is also in M. In French, the word "magma" has multiple common meanings, one of them being "jumble". It is likely that the French Bourbaki group... less