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Magma

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A magma (or a groupoid) is a set \displaystyle S, together with a function \bot : S \times S \mapsto S, i.e., a set with a binary operation \bot. A set \displaystyle S with an operation \bot that maps some proper subset of S \times S into \displaystyle S may be described as a magma with an operation not everywhere defined on \displaystyle S.

Magmas so general that usually one studies special cases of magmas. For example, monoids are associative magmas with an identity.

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