Magma (algebra)
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 equipped with a single binary operation . 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 Nicolas Bourbaki. The term groupoid is an older, but still commonly used alternative which was introduced by Øystein Ore.
| Algebraic structures |
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Group-like structures
Semigroup and Monoid Quasigroup and Loop Abelian group |
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Ring-like structures
Semiring Near-ring Ring Commutative ring Integral domain Field |
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Lattice-like structures
Semilattice Lattice Map of lattices |
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Module-like structures
Group with operators Module Vector space |
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Algebra-like structures
Algebra Associative algebra Non-associative algebra Graded algebra Bialgebra |
Read more about Magma (algebra): Definition, Types of Magmas, Morphism of Magmas, Combinatorics and Parentheses, Free Magma, Classification By Properties, Generalizations